Chater: "The Avalanches has always been different things at different times. Sometimes it is people DJing, sometimes it is a band. We want to keep that going." The Avalanches are ready to face their public again. Di Blasi: "It's gonna be us playing instruments quite badly but hiring some really good musicians to make us look good. Dropping our own records, that party vibe. Just like we do." Chater: "We want to do everything!" Di Blasi: "We want to run for president!"

A lot of things have changed since the year 2000, a lot of things have not. That was when perhaps the most cultish and elusive cult band in the world – based in Melbourne – released Since I Left You, rightly acclaimed as a landmark millennial album blending sample-driven hip-hop beats with a psychedelic, tropical backbone. A butterfly flag heralds the arrival of the new Avalanches album. It was revolutionary at the time and still is, both technically and for the pure emotions expressed. It won six Australian dance music awards, went top 10 in Britain and got them an ARIA award. But beyond that, it was an album of finely drawn feelings: it seemed, like all great collections of music, to promise something close to salvation, reassurance and enlightenment. It was that good. What's changed in 16 years? The people. The Avalanches is now just Chater and Di Blasi with wingman James de la Cruz sometimes there, sometimes not. Since I Left You's turntablist Dexter Fabay, founding member Darren Seltmann and multi-instrumentalist Gordon McQuilten all drifted away with the sense it was not going to happen quickly. "Darren realised before we did that another Since I Left You wasn't going to roll around in a couple of years," says Di Blasi. "This path it took us to go on was pretty difficult and it hasn't been a normal life."

What hasn't changed? The sound. The first single, Frankie Sinatra, a bouncy, festival-ready hip-hop track with US rapper Danny Brown rhyming over the sampled 1940s calypso of Wilmoth Houdini, is pretty much unrepresentative of Wildflower, and it seems almost at odds with the mixtape sonics of the band to actually release singles, removed as they are from the continuous flow of the album. Yet Wildflower is unmistakably and utterly The Avalanches; no one else could make a record like this. So why the hold-up? Sixteen years is generational change. "This is just such a strange moment," says Chater. "I can't believe we're sitting here with you talking about it." Even the mixing of the record – the post-production– took five years. Clearing the samples for legal use also took five years. Slowly other people joined the project; some of the all-star guests have been in for the long haul, waiting until the time was right. These are, among others, Danny Brown, foundation hip-hop artist Biz Markie, Father John Misty, Jonathan Donohue of Mercury Rev, MF Doom, Toro Y Moi, Warren Ellis and Jennifer Herrema of Royal Trux. "We were isolated within ourselves for a long time," says Di Blasi. "Then 'holy crap – this is really happening. It is actually going to happen. We did it.' But there's always this thing in the back of my mind something will happen to stop us. It just went on for so long."

The record is out through XL (Jamie xx, Basement Jaxx) in Britain and EMI in Australia. The record was all but done when previous Australian record label Modular – run by Sydney music identity Steve Pavlovic – fell over after a bitter split with its parent company, the multinational Universal Music, over claims of $US450,000 in unpaid royalties to the Perth band Tame Impala. "We thought 'we are not going to get this done'," says Chater. "Then we almost would get it done. Then something would happen." They worked on an ambitious but ultimately doomed animation-and-music project for two years. The scale of it was massive. It was to come out under The Avalanches' name as a feature-length animated movie made with hand-drawn cells, done by an illustrator in South Korea, and with Avalanches' music. "It was inspired by Yellow Submarine," says Chater, "and 1960s Japanese pop-art. Like a cartoon for grown-ups. It was going to be this big, beautiful hand-crafted thing, a really fun psychedelic, hip-hop cartoon." But it was funded privately, and very expensive, and the money fell through at the last hurdle.

Four years ago The Avalanches got involved with famed English producer and composer Marius de Vries, who a long time ago was in The Blow Monkeys. But he has also worked with Coldcut and Bjork's The Sugarcubes, and he was doing the music for a theatre version of King Kong. The Avalanches were down to do three of the songs for King Kong, but in the end did one. "All of these things had to happen in order for us to get here," says Chater. "Now I can see it was all necessary but it was just a crazy long way to go about it." Chater grew up in Werribee in Melbourne's western suburbs, and met Di Blasi in the central Victorian town of Maryborough in the '90s. Both had long hair and were into metal and grunge and they ended up sharing a house in Melbourne when the earliest incarnations of The Avalanches emerged. The two shared a room and had a tape player with one cassette and on it was Across The Universe by The Beatles, still an Avalanches touchstone. "We listened to it again and again," says Chater. As a rambunctious, Beastie-Boys styled collective with floating membership, they released their first EP in 1997. Then Since I Left You in 2000, a seismic shift. Instead of following it up, they retreated, yet kept making music on the quiet, unsure of what to do. "I have always made music since I was a kid," says Chater, "and a certain amount of music came together at a certain time which was Since I Left You but there was all sorts of other music floating around before then of course; we just kept making music."

He and Di Blasi holed up at Chater's home studio in Melbourne and made what Chater calls "George Harrison, droney, psychedelic, psyched-out, Beatles-y Across The Universe guitar music". Luke Steele was involved, singing, after Sleepy Jackson but before Empire of The Sun. The project went nowhere but snatches of the music remained. Elements of it – and King Kong, and the animated movie album – all found their way into Wildflower. "A few years of making droney music," says Di Blasi, "and we were like 'we need to get happy again!' Let's make something that will make people smile instead of just sit there and bliss out. It was just exploring. We didn't know where we were going. Then we went back to the more sample-based hip-hop ideas." As time wore on, deadlines were set but missed. The idea emerged to release an album 10 years after the last: 2010. "Eight years became 10 years became 12 years, then 16," says Di Blasi. "We thought 10 was a long time. Now it's 16, which is crazy." Di Blasi was out DJing in Melbourne one night when a young guy approached and asked him if he used to be in The Avalanches. "My mum loves your band," the young punter said. "At that point," says Di Blasi, "I thought 'OK. It really has been a long, long time."

The trickiest sample to clear was a portion of a kids' choir singing Come Together by The Beatles for the song Noisy Eater, which also samples the '60s teen musical Putney Swope: the general rule is you can't sample Beatles' music because the owners – Paul McCartney and Yoko Ono – don't allow it. So the pair wrote a letter to the other pair outlining the spirit of what they wanted to do, stressing it wasn't gratuitous, but respectful. The letter was "heartfelt", says Chater, and it worked. Slowly a narrative for the album emerged, and a long process of stripping away the excess, and there was a lot of excess. When Wildflower was first played to close confidantes, including members of electronic band Cut Copy, the feeling was the beauty, the joy and the transcendence was hidden. "We started stripping it back," says Chater, "and started to see the beautiful core that had become obscured." For at least 10 years the "will-they-or-won't-they" story of The Avalanches' return has taken on a mythical quality in culture magazines, online forums and social media, feeding on huge public anticipation. Even the 25-second song for King Kong was eagerly devoured as a totem of what might lie ahead. Then last year and into this year it hit fever pitch as the wheels of the slow-turning machine ground up a gear. Two months ago, information started filtering out from seemingly official sources that something was up. Since then it has been a drip feed of songs, imagery and video, some leaked, some official. And then, it was done. But what is Wildflower? It's a wildly psychedelic dreamscape with sounds and ideas and flashes of colour and shifting moods that wash in and out of each other in an astonishing, seamless continuum. It is technically incredible, perfectly structured, a story, in a sense, without a clear beginning or end.

From the first notes of the first track – The Leaves Were Falling, which becomes Because I'm Me – we are in familiar territory, the poignant sample of a little boy singing, taken from a 1950s recording of children from New York housing projects. If anything, Wildflower is better than Since I Left You. It's more diverse, more detailed and funkier, but with that same intangible, emotive quality that came before. Some of the samples are fascinating: Chandra, an '80s punk-funk singer from New York. The Bee Gees' version of Warm Ride. Dialogue from a documentary about painter Jean-Michel Basquiat. Late '60s psychedelic band Spirit. The lost 1980s disco-funk of Gene Dunlap. Chater, Di Blasi and de la Cruz are certainly perfectionists. Obsessives. The kind of music they make – in kaleidoscopic, shifting layers – demands that. They are also pure musicians in that they make music for no known end most of the time; an accumulation of ideas and pathways. Those who work with them say they like to micro-manage every aspect of what is being done with their music and the imagery that goes with it. The key point seems to be that they are seeking an almost impossible quality in their music: a conflicted emotion. "For me," says Chater, "the parts of Since I Left You that were really successful had that feeling of happiness but where sadness meets it, that bittersweet thing where it hurts a bit. "The party stuff is very easy to do, it flows, it's quick. It's not so much of an accomplishment. The other stuff is harder to do, to hit that beautiful feel and tone, which is why I love the Beach Boys. That sweet spot where it's happy and sad at the same time."

The record on one level is a kind of imagined travelogue, full of snatches of conversation, traffic sounds and interludes within interludes. "The characters are escaping reality," says Chater. "Going to the desert or going to the sea. We wanted it to be carefree and chaotic and joyful. Something a bit loose and riotous." He talks about a "home-made hobo-spirit", about the power of music to heal and change lives. "Also sincerity," he says, "and truth. "You can work from your thinking brain where it is intellectual and analytical but we are never successful when we work from that place. So it's about finding a truthful feeling. It's always been about chasing a feeling for us." Wildflower is released on July 8.