When three battered ex-junkies from Guns N'Roses got together to form Velvet Revolver, the cynics got ready for a flop. Guitarist Slash tells Adam Sweeting about going straight, going steady and making the critics eat their hats

It probably wasn't Atlantic City that Guns N'Roses had in mind when they wrote Paradise City. The latter was a vision of a debauched rocker's nirvana "where the grass is green and the girls are pretty", but Atlantic City barely lives up to its billing as a tasteless parody of Blackpool.

It's a grim cluster of fast-food outlets and concrete-slab casinos advertising cabaret turns by Wayne Newton or Patti Labelle, and the fabled boardwalk looks like a shopping mall that never got finished because the contractors went bankrupt. Some say the Mob tossed the corpse of union boss Jimmy Hoffa into the marshlands alongside the highway.

Yet this is where Guns N'Roses veterans Slash, Duff McKagan and Matt Sorum find themselves on a sultry summer Saturday in June. They're here with their new band Velvet Revolver, in which they're joined by vocalist Scott Weiland (formerly of Stone Temple Pilots) and second guitarist Dave Kushner.

Atlantic City is the last stop on their debut American tour, a string of gigs that kicked off at the Roxy in Hollywood before scorching across the US. They're headlining the first day of a weekend mini-festival at Fantasy Island, which turns out to be a patch of waste ground behind the parking lot of the Borgata casino resort, with Budweiser tents and the kind of amusement stalls where you throw a ball at a target to send a girl in a bikini tumbling into a tank of water.

Cynics predicted that Velvet Revolver's alliance of battered ex-junkies - in Weiland's case, the "ex" part is in rather faint lettering - would disintegrate before it left the runway. Hence, there was a noise of hats being eaten when VR's new album, Contraband, sold 250,000 copies in its first week, barging the smarmy Usher off the number one slot and trouncing the combined sales of new greatest-hits compilations from Guns N'Roses and Stone Temple Pilots.

"You sort of have to expect no matter what you do that there's going to be this negative thing that comes with it, and people's preconceptions of what you're doing," drawls lead guitarist Slash, making inroads into a bottle of burgundy in the band's dressing room. "God knows I had to deal with it with Guns N'Roses the whole time."

For once, the guitarist has pulled his mass of tumbling black curls back from his face so you can actually see what he looks like. Despite having survived snowdrifts of drugs, lagoons of Jack Daniel's and groupies tumbling out of wardrobes, Slash seems younger than his 40-odd years.

"The kids, the actual fans, were feverishly talking about Velvet Revolver because I think they needed a new shot in the arm as far as rock'n'roll was concerned," he continues, "but then of course there was the buzz from inside the music industry which was, 'Oh, Scott's a fucking heroin addict and Slash and those guys are all washed up,' but they all were watching us, y'know? But once we were onstage the only people that really mattered for us were the people who'd bought a ticket."

One mogul who thought he could sniff a phenomenon on the wind was RCA's Clive Davis, the man who shaped the careers of Janis Joplin, Whitney Houston, Alicia Keyes and Carlos Santana (twice), and the only non-performer ever inducted into the Rock and Roll Hall of Fame. Davis flew to LA and drove out to the band's rehearsal studio, to find out, says Slash, whether they were serious or "if it was just a bunch of elements plucked out from superstar bands and put together as a fabricated fuckin' thing". Davis swiftly concluded that the Revolvers were the boys he wanted, though since we're talking about three-fifths of the biggest-selling rock band since Led Zeppelin, this can't have been one of his most difficult decisions.

"We ended up going with Clive because his deal was maybe not the best one but it was good enough for us," says Slash, "and he was old-school enough that we'd feel comfortable with a record company that he was running. It turns out some of the other people that were shooting big numbers at us are now no longer employed, so we made the right move."

For the former Gunners, Velvet Revolver represents a dramatic role reversal. Where Guns N'Roses was like a wagon-load of nitroglycerine rattling towards a precipice, VR is more like a therapy group. Slash is the only one who still drinks, and the tour manager carefully sweeps the backstage area clear of alcohol before the others can find it. Where once you would have found the Gunners lying face down in a trough of cocaine (or worse) before a show, a drugs ban is strictly enforced.

Fables of Slash's wild years could fill several volumes, and he recounts his yarns with the affable nonchalance of his hero, Keith Richards. "The one where I died in San Francisco? I remember exactly what happened. These drug dealers came to my hotel room at 5am. They had everything and I took all of it. I started down the hallway and I ran into a maid, and I asked where the elevator was and then bam! I collapsed. Little Spanish lady, it freaked her out. When you overdose, there's a certain kind of scene where everybody is just moving really quickly and there's noise from radios and everything; I've experienced it a bunch of times. They took me to the hospital but I said, 'I'm fine', signed myself out, went back to the hotel and we flew to the next gig."

In the decade since Guns N'Roses, they've all changed in different ways. Drummer Matt Sorum has explored new avenues in arranging, production and composing. A burst pancreas suggested to bassist McKagan that it was probably time to quit boozing, and he straightened his head out by going back to Seattle to take a degree in finance. Like McKagan, Slash has become an enthusiastic husband and father, and had just flown in from LA , where his wife had given birth to their second child.

"I woke up the other day in my hotel room and I was going, 'God, I'm so glad I don't have some stoopid bimbo I gotta kick outta here from last night, y'know?" he says. "After a while you've done it too many times and it just gets old." Your missus probably worries about you on the road? "She doesn't worry about me, she'd kick my ass," he chuckles.

"But I was married once before and I must have been the worst husband you could possibly have. I used to keep three or four different hotel rooms in the same hotel so I could go back and forth to different girls. Matt [Sorum] really thought I was sick; he thought I needed treatment for sex addiction. That's when I met my current wife. We were always really good friends and we used to fuck around here and there. Then I ran into her just before my divorce and we've been tight ever since."

Scott Weiland is the biggest cause for concern, following years of heroin addiction, arrests for possession and enforced spells in rehab. Weiland was allowed out of his lock-down facility in Pasadena under police escort for four hours a day to record the Contraband album, and was drug-tested every evening on his return. Although clean for a couple of months now, he still has to report regularly to a counsellor in LA.

The band fell together after Slash, Duff and Matt all turned out to play at a benefit concert in 2002 for ex-Motley Crue drummer Randy Castillo, who died from cancer. They enjoyed playing without crazy control-freak Guns N'Roses vocalist Axl Rose so much that they started making plans, and when they were hired to write Set Me Free for the soundtrack of The Hulk, they went looking for a singer. They had heard Weiland had split with Stone Temple Pilots.

"We knew he was loaded," says Slash, "but he showed up and he sang great, but he did have this gigantic fucking enormous monkey thing happening, and so we talked about it. He admitted he had a problem and wanted to work on it, and we said, 'Look, we've all been there, probably worse than you have, so if you want some help we'll help you,' and we just worked through it together. We were doing it one step at a time and we didn't have any visions of the future."

Weiland may be their biggest liability, but he also adds a vital whiff of volatility. His lyrics bring a sense of wrung-out personal turmoil to the VR songs, not least in the self-loathing onslaught of Big Machine ("He's a junkie piece of shit because he says so") or the album's grandiose mega-ballad, Fall to Pieces, where Weiland plays the spectator crushed by the falling debris of his own life. "The record is really a snapshot of that year, from June 2002 when we met Scott up to October last year when we went in the studio," says Slash. "With Scott and his lyrics it's a very personal thing. I don't think any of us would want to go there unless he asked us."

The Contraband album is a smartly conceived mix of punk attitude, road-drill riffs and shrieking metal, but with plenty of hooks and harmonies to sweeten the dose. Onstage, the quintet teeter along the tightrope between passion and pastiche, with Slash spinning backwards across the stage in mid-solo with a cigarette clamped between his teeth, and Weiland wiggling and mincing as if raising a defiant digit to the entire history of heavy-metal machismo.

Sometimes they strike a pose on a plinth, centre stage, Slash holding his guitar up vertically, Weiland frozen with arms aloft, and McKagan shaking his blond mane and displaying his chiselled physique. Their final song is the Guns N'Roses heroin anthem, Mr Brownstone. Not, we trust, the shape of things to come.

· Slither is out on July 12. Velvet Revolver play the Academy, Glasgow on August 31, the Apollo, Manchester on September 1 and the London Apollo on September 2. Box office: 0870 771 2000.