'I got the fortunes of heaven

in diamonds and gold

I got all the bonds baby

that the bank could hold'

'Ain't Got You' – Bruce Springsteen

In 1987, when Bruce Springsteen wrote the song "Ain't Got You", he was the biggest rock star in the world. He had vast estates in New Jersey and Beverly Hills, and he had not long returned from a honeymoon at Gianni Versace's villa in Lake Como. "Ain't Got You" was Springsteen's attempt to make a self-aware nod to his outrageous fortune, the Rembrandts on his walls, and how he had come a long way from his working-class upbringing.

Before he released it, Springsteen played "Ain't Got You" to Steve Van Zandt, his best friend since they were teenagers and a key cohort in his E Street Band. Van Zandt was appalled. "I'm, like: 'This is bullshit,'" he recalled telling Springsteen. "'People don't need you talking about your life. Nobody gives a shit about your life. They need you for their lives. That's your thing.'"

The argument came back to me as I waited to meet Matt Damon. If Springsteen is the voice of the American heartland, channelling its concerns and its struggles, then Damon is the physical embodiment. In a career that started for most of us in 1997 with Good Will Hunting, a film that he co-wrote and starred in with his childhood friend Ben Affleck, the 42-year-old actor has specialised in playing the everyman. His most enduring roles – from the eponymous hero of Steven Spielberg's Saving Private Ryan to the ex-CIA assassin with amnesia in three wildly popular Bourne movies – have traded on his skill to be relatable to a mass audience. And, quite simply, no one does it better: the US business magazine Forbes found in 2007 that for every $1 Damon was paid, his films made $29 of gross income – the best return in all of Hollywood. He is the all-American movie star.

This afternoon, at a hotel in a frigid, snow-dusted Berlin, where Damon is appearing at the film festival, he is taking his representation of the Average Joe to Method extremes. He wears jeans and a fleece. (Yes, a fleece. Try for one moment to imagine Brad Pitt wearing a fleece; it's not possible.) He has rimless glasses, which may be designer but have no obvious branding, and clumpy work boots. He will tell me later that one of his least favourite parts of the film process is the pre-shoot costume fitting. "I try to get in and get out as fast as I can," he says. "When we get to the shoes, I get the most comfortable shoes that I can, because I don't want to stand around all day in shoes that nobody is going to look at."

Damon is presumably enviably stacked – he runs, lifts weights, hits pads occasionally – but that is not immediately obvious to look at him. He may be paid £10m to star in a film, but he seems like the kind of guy who would blanch at spending more than £10 on a haircut. The comedian Sarah Silverman once said of him: "He doesn't need a fancy accent or a fake tooth to play a 'regular person'." People often come up to Damon and tell him he looks just like their brother.

Of course, like Springsteen, Damon now has very little in common with the average American – if indeed he ever did. His father, Kent, was a stockbroker and his mother, Nancy Carlsson-Paige, is a well-regarded professor of early-childhood education. His parents separated when he was two and he and his older brother Kyle were raised by their mother in a sprawling six-family co-operative household in Cambridge, Massachusetts, a city best known as the home of Harvard University and MIT. One of Damon's regular babysitters was Howard Zinn, a radical historian whose 1980 book A People's History of the United States is credited with redrawing key events of American history.

When Damon was a teenager, he went backpacking with his mother on her research trips to Guatemala and Mexico, living with local families, speaking Spanish. After school he won a place to study English at Harvard. He was in his final year of studies when he decided to leave university for Los Angeles. It was 1992 and he was convinced that a part in the movie Geronimo: An American Legend, alongside Jason Patric and Gene Hackman, would be his big break. It wasn't. But eventually he poured his experiences from Harvard into the script of Good Will Hunting, the story of a janitor at MIT who is a maths savant. He won an Oscar for best original screenplay, and there has scarcely been a lull or a dud film since.

Is Damon, I ask him in Berlin, a fan of Springsteen? It turns out to be a lucky guess, made only because his new film is called Promised Land – the name of a track from the 1978 album Darkness on the Edge of Town – and by the fact there is a memorable scene in the movie where Damon's co-star John Krasinski sings a karaoke version of the song "Dancing in the Dark".

"Uh-huh, huge," says Damon. "Springsteen's a god in my eyes." There then follows a few minutes where Damon picks his way excitedly through Springsteen's recent oeuvre: The Rising ("a masterpiece"), Magic ("such an intelligent takedown of the Bush administration"), and culminating with last year's Wrecking Ball, which reached number one in both the UK and the US. It is an intensely political record that shines a harsh light on the American dream, with music inspired by the Civil War and the Dust Bowl. "It doesn't feel like an act," Damon muses. "It doesn't feel like he's trying to pretend that he still has the common touch. I think he believes what he believes, and that's very real."

He continues: "I do view this movie, Promised Land, as the visual expression of his last album. It's actually eerily similar. I hadn't heard the album before we wrote the script, but John Krasinski and I went to hear him in Madison Square Garden at the first show that he did of Wrecking Ball and he played the album and I went: 'Fuck! That's the movie!' I went back to see him afterwards and he asked: 'What are you working on?' And I said: 'It's like the movie version of your new album.' And he goes: 'What the fuck does that mean?' And I said: 'I don't know, man! But you've got to see this thing when it comes out. I'm telling you, it's the movie version of your album.'"

Promised Land is the first proper full-length script that Damon has completed since Good Will Hunting. He would have liked to write more over the years, but his acting career took off, then he got married in 2005 and now he has four children, all girls. That Promised Land exists at all, Damon concedes, is down to the determination of his co-writer Krasinski, an actor who starred in the long-running American edition of The Office; he played the "Tim" character (who was renamed Jim Halpert). Krasinski would show up at Damon's house at 8am each Saturday and they would write all weekend, only breaking for meals and obligatory screenings of The Little Mermaid with Damon's kids.

‘My wife’s a civilian and that takes a lot of pressure off’: with Luciana. They met in Miami in 2003. Photograph: MCMULLAN CO/SIPA/Rex Features

Family time is non-negotiable for Damon. He met his wife, an Argentinian-born bartender called Luciana Bozán, while he was shooting the comedy Stuck on You in Miami in 2003. Luciana – whom Damon calls Lucy – already had a six-year-old daughter, Alexia, and they have since had three girls together: Isabella, Gia and Stella. The family have a two-week rule, where they will not be apart for any longer. Damon is completely unyielding on it: when he shot Invictus, he flew out Alexia's entire school class to South Africa and organised for them to do a special project on Nelson Mandela. Damon's advice on living in a household of five women is simple: "Find yourself a little man area."

Krasinski's original idea for Promised Land was to create a film about what he called "American identity", and the break-up of small communities, and he worked with the author Dave Eggers to produce a basic outline. Damon took over from Eggers, and the focus of the script became the response of a small town to the arrival of wind turbines – taking the 1983 British film Local Hero as an inspiration. This idea was working perfectly until Krasinski and Damon found out that the dramatic tension they had created on the page did not exist in reality.

"We visited this town and realised that none of it was true," says Damon. "We had built the mansion of our dreams on a foundation of clay, basically. It was at that point, which was devastating because we thought that the movie was going to go away, that my wife said: 'I've never seen you this happy. Even if you don't make this movie, think of how much fun you've had for the last three or four months.' I'd forgotten that feeling of pulling ideas out of thin air and bouncing them off a friend – and just how much you laugh."

Promised Land was saved by an eleventh-hour switch from wind farms to hydraulic fracturing, a contentious technique also known as fracking that is a hugely divisive issue in the States already and increasingly now in the UK. Fracking involves drilling miles into the earth and pumping in a pressurised mixture of water and chemicals in order to break up a layer of shale and release the natural gas inside it. Environmentalists claim that fracking contaminates drinking water and causes numerous other ills; energy companies retort that they have been doing the process for 50 years with only minimal effects.

But Promised Land is not really a polemic about fracking – which, Damon concedes, is unlikely to send box-office registers spinning. It is instead a powerful morality tale, spliced with moments of comedy and romance; the writing is sharp, and the cast (which also includes Frances McDormand and Hal Holbrook) is uniformly excellent. Damon plays Steve Butler, an employee of the drilling company who has to convince the hard-luck local residents that their lives will change for the better if they lease their property to him. Steve is brilliant at his job; he has an innate ability to reassure people that he shares their dreams and their fears. But this should not come as a surprise – it's a performance that Damon, as an actor, has been honing all his working life.

Matt Damon has been thinking about Good Will Hunting more than usual recently. It's partly because he'd been writing again, partly because the film has just celebrated its 15th anniversary and partly because Promised Land – like Good Will Hunting – is directed by Gus Van Sant (they also worked together on a semi-improvised movie called Gerry). Van Sant was asked recently how Damon had changed in the past decade-and-a-half; he replied: "Not too much. He's older. He's pretty much the same."

I put the same question to Damon: how is he different now? He scrabbles around for a few moments, uncharacteristically blustery, throwing out platitudes about working with some great people and learning a lot about the business of movies. "But I feel fundamentally the same," he decides. "When you're 16, you kind of know who you are. I don't think there's too much that changes."

Eventually Damon settles on one big difference: he doesn't smoke any more. This might not sound like the most meaningful development, but that would underestimate the intensity of his devotion to the habit: a pack-and- a-half a day for 17 years. He recalls the day he stopped – 5 August 2004 – almost as if it was the birth of a child. "Ben and I started when we were in high school. We'd see the great actors – Brando, James Dean, Mickey Rourke, who we loved back then – smoking, and we just thought it was fucking cool."

So what made him stop? "Life," he says, flipping the cap on a bottle of Diet Coke. "Actually, I remember my brother gave up before he had kids and he said: 'I'm going to give myself six months or a year to clear out my system before I, you know…'" Damon suddenly becomes a little coy. "Whether there's any wisdom to your sperm-carrying, your system being somehow cleaner, but that was his thing and I remember thinking: 'Yeah, I'll do that, too.' Lucy and I knew we'd be having more kids and that process started a year later."

Damon laughs; he appears unsure how we've alighted on the subject of the motility of his sperm. He has traditionally been reluctant to get too personal in interviews, but today he is relaxed and unguarded. Still, he admits to having conflicted feelings about his own celebrity, from Good Will Hunting onwards. "Fame is really strange," he says. "One day you're not famous and then the next day you are, and the odd thing is that you know intellectually that nothing in the world is different. What mattered to you yesterday are the same things that matter today and the rules all still apply – yet everyone looks at you differently. So the surreal part of it is that the world is exactly the same, but it is completely different for you. The way you experience the world is never the same again.

"It's why a lot of people freak out or they become megalomaniacs," he continues. "They feel it's all about them, but there's this disconnect, because they're going: 'Wait a minute, the earth still moves around the sun – what the fuck?' There's no handbook for celebrity, the surreality of it. You can't really explain it until it happens because it's such a mindfuck; it's such a bizarre experience."

Friends indeed: with Ben Affleck in Good Will Hunting. Photograph: Allstar/Miramax/Sportsphoto Ltd/Allstar

Few people have had a better view of the negative impact of fame than Damon, forced to watch from the front row as the career of Ben Affleck, his "hetero lifemate", was destroyed by gossip magazines when he was dating Jennifer Lopez between 2002 and 2004. "I would talk to Ben during that time and he'd go: 'I'm in the absolute worst place you could be – I can sell magazines, but not movie tickets. It is jail. I'm totally fucked right now.'

"Our agent, Patrick, called the editor of US Weekly and begged her to take him off the cover. He said: 'I promise you there's nobody in New York or LA who wants to see Ben on the cover of a magazine any more.' And she goes: 'You're right, but it's not my fault that everyone between those cities does still.' And they literally kept him on the cover until every single person in America was like: 'I can't stand this guy.' And that was 10 years ago. It took him 10 years of really hard work to climb back up the mountain."

I meet Damon before Affleck's latest film, Argo, which he directed and starred in, wins the Academy Award for best picture, but it is clear he has a proprietary pride in his friend's comeback. After years of living in New York, Damon has just bought a house down the street from Affleck in Los Angeles. He says they are working on a few projects together through their production company Pearl Street Films, the most advanced of which is a biopic of James "Whitey" Bulger, a vicious Mob boss from Boston known locally for his Robin Hood acts of philanthropy. Damon is set to play Bulger and Affleck will direct.

Affleck may have spectacularly turned his career around, but Damon notes that there is a still a handful of paparazzi stationed day and night outside Affleck's house, where he lives with his wife, Jennifer Garner. "A lot of it boils down to luck: my wife's a civilian and that takes a lot of pressure off," says Damon, who previously dated Minnie Driver and Winona Ryder. "It's really sex and scandal that moves those magazines, and there's nothing scandalous about a guy who's married and has kids. If they come outside where I live, they are going to die of boredom – there's just nothing really going on that would sell a magazine."

Damon – again, similar to Springsteen – has been drawn to edgier, more provocative material as his career has become more established; whether his personal sensibilities match those of the typical American cinema-goer is almost a moot point. Promised Land is not an explicitly political film; in fact, probably the highest compliment is that it has already taken flak in the States from the mining companies and the anti-fracking environmentalists. When both groups feel that the action shows favouritism to the other, it's a decent indication that a balance has been struck.

Off-screen, though, Damon has not been so reluctant to speak his mind. He was a vocal supporter of Barack Obama in 2008, but cooled before the last election, saying: "A one-term president with some balls who actually got stuff done would have been, in the long run of the country, much better." President Obama used the White House Correspondents' dinner in 2012 to respond directly: "Matt Damon said he was disappointed in my performance. Well, Matt, I just saw The Adjustment Bureau…"

Damon is undeterred; he is also the co-founder of a charity – Water.org – that uses microfinance loans to improve water sources in Africa and India. (At an American Cinematheque dinner for Damon, the actor Ben Stiller said: "You don't screw around. You went out and claimed water. I mean, that's, like, an element!") The director Michael Moore has suggested that Damon run for president himself.

He shakes his head. "The values that I have are the values I was raised with, from where I'm from, which is a middle-class place," Damon says. "So that informs everything about me, my politics and all that stuff. I mean, politically I vote against my own self-interest at every election. I actively ask these people to raise my taxes. But I believe a solid, really strong middle-class is the key to making the country in the best way."

There is evidence that Damon will continue taking more risks with his work. He has recently completed a biopic of Liberace called Behind the Candelabra. Despite an enviable roster of talent – Michael Douglas is Liberace, Damon plays his long-term partner Scott Thorson, and Steven Soderbergh directs – the film was turned down by every major US movie studio for being, in Soderbergh's words, "too gay". Eventually the $5m budget was covered by the cable channel HBO, and it will be aired in the States next month and in the UK not long afterwards.

Damon admits the film will not appeal to everyone – "They can change the channel" – and that it was a stretch, at least initially, for him to play a part that involved nakedness and impassioned clinches with Michael Douglas. "What really helped was the clothes and the hair," he says, smiling. "I had four different wigs and these phenomenal outfits, and they really helped the way that I stood and the way I walked. It was like osmosis; I totally got into it." (Soderbergh agreed: "It was great to see Michael and Matt jump off the cliff together. Nobody can accuse them of being shy. They just went for it.")

Time is up, the Berlin film festival premiere of Promised Land awaits, and Damon might need something smarter than his jeans and fleece. But before he leaves, I ask him what he makes of that dispute between Bruce Springsteen and Steve Van Zandt 25 years ago. His answer is revealing about his own career. "Steve Van Zandt is right," says Damon. "If you're trying to play an everyman, you've got to have the same concerns and be struggling with the same issues as the people who are coming to see the movie. A movie about a narcissistic, rich movie star would not work, unless you were making a take-down. If you are writing a story and trying to draw an audience to come and hear you tell it, it's got to in some way relate to them. Who wants to come and hear about your specific problems? It's not therapy – it's supposed to be a communal piece of entertainment."

In other words: Damon's not going to have an "Ain't Got You" moment any time soon.

Promised Land is out on 19 April