A couple of years after he won the 1998 Turner prize, Chris Ofili was in Atlantis art store in the East End of London, buying huge quantities of paint and holding up a queue. When he handed over his credit card, the cashier recognised his name and struck up a conversation about his work. A student standing behind Ofili then joined in with some excitement.

"Are you Chris Ofili?" he asked. "In art school, the word was you'd given up."

Ofili was delighted. "Go back and tell your friends that I've definitely given up," he replied. "Just don't tell them you saw me buying this much paint or they won't believe you."

Ofili, 41, has always struggled with success. Not achievement. For that he has worked hard and, unlike most young artists, his efforts paid off almost immediately. Before he was 30, his work had been exhibited on three continents, including solo shows in London, New York and Berlin, he was in Charles Saatchi's Young British Artists collection and he had won the Turner prize. In the intervening decade, he's had the British Pavilion at the 50th Venice Biennale, the Blue Rider, Devil's Pie and Upper Room exhibitions – to name but a few. At the end of this month, Tate Britain will put on a mid-career retrospective, exhibiting a selection of his work up to the present.

But it is the renown that comes with this success Ofili has found troublesome. "I'm aware that success can overwhelm you," he says. "The perception of you can be elevated to such a status that it's not you any more. But you start playing you. You have to leave the real you at home because the fake Chris Ofili has been invited to dinner. I was being invited to all kinds of functions and meeting all kinds of interesting people. But I went to very, very few because it was hard to be the person they thought I was. People were asking me to say things. I'm a bit more irresponsible than that. Sometimes I prefer not to have read the latest book but to have been really following Man Utd. Not that that can't fit. But it made me feel uncomfortable that it might not. There was a point in time where the thought of people even talking about me made me anxious. Physically."

That point reached its apogee in 1999 when his work gained global attention after New York mayor Rudy Giuliani took umbrage at Ofili's Holy Virgin Mary painting hanging in Brooklyn Museum of Art. The painting depicted Mary as a black woman with an exposed breast made from elephant dung and surrounded by cutouts of female genitalia from pornographic magazines which looked from afar like small butterflies. The mayor threatened to withdraw funding for the museum, and lost a lawsuit in which he tried to censor its choice of artists. When a federal court ruled that this would violate freedom of speech, Giuliani responded, "There's nothing in the First Amendment that supports horrible and disgusting projects!"

Thrust, unexpectedly, into the glare of global media, Ofili decided to say nothing. "I just thought, what's the point of throwing anything out there at all? I've already done the painting and they're going to work that to mincemeat. Then, as time passed, I thought it would be more interesting to be in the audience than on the stage. I was actually scared as well. It was this American rage. I was brought up in Britain, I don't know that level of rage. So it was easier and perhaps more interesting not to say anything. I'm still glad I didn't."

The moment proved pivotal in terms of how he would navigate the relationship between his work, his renown and his life. "That's when I started to feel hemmed in," he says. "That's when I thought it's time to turn the music off, turn the lights on and say, 'Party's over. Go tell the rest of your crew.'"

Neither stoic, ascetic nor reclusive, Ofili became driven by a dual desire to protect his art and his sanity. You get the impression he needs to be forgotten if only to produce memorable work. There would be relatively long fallow periods where he would not do solo exhibitions for several years. "The studio is a laboratory, not a factory," he says. "An exhibition is the result of your experiments, but the process is never-ending. So an exhibition is not a conclusion."

When he does exhibit, his work is generally greeted with qualified critical appreciation that falls just short of full-scale acclaim. "Amid intense critical scrutiny and the distorting glare of the market, Ofili is doing something quite bold: he's giving up his formulas and looking for new forms," wrote New York Magazine. "He wants you to see the arc of a career... not just chart-toppers."

Why wouldn't he just stick with the chart-toppers, develop the styles and themes he knows work and win awards? "I'm not after a type of refinement of your life with a view to writing your own obituary," he explains, "summing up as early as possible so people get it and they can just slap you on the back every time they see you. I just want to see what I can get out of this whole thing."

At times it seemed like the main thing standing in the way was the trappings of success. "People kept asking me to do things," he recalls, "but there's more than one way of achieving, and you have to use your own measuring tape."

He was invited to be a member of the prestigious Royal Academy, but couldn't fathom any way in which it would be beneficial for him or his work. "Does it come with a parking space outside the Royal Academy?" he asked. "Because, if not, I can't see anything in it for me."

"It's a great honour and you'd be the first black RA," his suitor explained.

"I'll probably be the last one, too, once you get to know me," he said.

Having made his name and some controversy with elephant dung, Ofili thought it was time to get his shit together. "I felt I'd achieved quite a lot in London in a short space of time. That's a really good thing. But in doing that, I had a sense I could see where it was all going. I couldn't see that many surprises on the horizon. There was a familiarity with myself that I didn't really welcome. It was all getting a bit obvious. I wanted to feel that my life was being enriched because I was achieving, but I didn't feel that I could do it in London. "

We are talking on the veranda outside his studio, halfway up Lady Chancellor Hill in Port of Spain, Trinidad and Tobago, where he moved in 2005. As dusk falls over the nearby mountains, joggers and walkers from the huge Savannah park climb the hill, signalling not a parade of new year's resolutions but the approach of carnival season. It's not difficult to see why someone would want to live in Trinidad. But it's not immediately obvious why Ofili in particular would want to live there, either. Born and raised in Manchester, Ofili's parents are from Nigeria; his partner's family are from Egypt. He listens to the BBC World Service, watches Premier League games and gets the international edition of the Guardian.

So why Trinidad? The fact that neither he nor his partner had connections to the country was a bonus, because it made it neutral ground. He'd been invited there several years ago and had enjoyed it. "It instantly struck me as a place where I felt different, in a really good way, that I didn't fear. There weren't any signs telling me which way to go. It felt very free and open, a place where you had to discover things."

While eating dinner with his family (he has a three-year-old daughter and a newborn son), we heard the first sounds of carnival, as tunes from a steel pan band rolled down the Cascade side of Hololo mountain. Once the children were in bed, we drove over to see 10 men rehearsing a single refrain into the night. "I feel me here," Ofili said later. "I wonder if that's because the place is so unusual to me that I can become myself. I really ask very little of this place."

If he came in search of anonymity, he got it. When I told the immigration officer who I was coming to interview, I had to say the name three times, and even then she wrote "Chris Refifi".

Like his art, Ofili is an intriguing work in progress. With a beard and a few flecks of grey in his hair, he looks like a young, lean Danny Glover. His speech is measured, his voice soft with a Mancunian lilt. There is little in his upbringing to suggest the life he lives now was even possible, let alone likely. Raised in a working-class family in Manchester, he had little interest in art as a child and never went to galleries. By the time he was 20, he had been abroad only once, to the south of France by coach on a school trip he paid for with his paper round money. He left school wanting to be a furniture designer, only to learn, much to his annoyance, that he had to do a foundation course. "I took it on thinking I just needed to get a certificate. I'd never met artists before," he says. "I had no idea what that meant – to be an artist."

Then came Chelsea art school. "I don't think I met anyone posh until I went to London. I kept thinking, 'This person actually lives in Chelsea, on the Kings Road, and that's their car.' It really opened up my world." Throughout, his mother was concerned only with the basics. "All my mother would say is, 'Are you eating?' Not, 'Why are you studying art?' just, 'How are you going to eat?' "

He emerged on to the national scene with the help of two propitious tailwinds, thanks to the desire to rebrand Britain as cool and modern following New Labour's election in 1997. The first was artistic. Throughout the late 90s, the arts became far more popular and some young artists, such as Damien Hirst and Tracey Emin, started to act like rock stars, suggesting the dawning of a rowdy, vibrant new creative generation.

The second was racial. The publication in 1999 of the Macpherson report into the death of Stephen Lawrence helped pave the way for a brief moment when racial and ethnic difference was openly celebrated (before 9/11 and the onset of moral panic). Ofili won the Turner prize with No Woman, No Cry, a tribute to Doreen Lawrence with a portrait of her late son Stephen in each tear. "I thought it might say something," he says. "Not change anything, but maybe just say something." The same year, Goodness Gracious Me, an Asian comedy show, had its TV debut. The year after that Steve McQueen won the Turner prize. The year after that came Zadie Smith's White Teeth.

The notion that acknowledging race and racism would limit his appeal never occurred to Ofili. "I've always set out to embrace all that I am," he says. "Growing up in Britain at the time, when a major aspect of who I am was seen as negative, there was no way I was going to exclude that part of myself. Because then they've won. Or you've lost."

Nonetheless, he steered clear of the polemical. "A lot of black art that came before was set up to critique the system. I thought that was boring. Basically, you would have to be right all the time. And I was not interested in being right all the time. I wanted to be sincere and outrageous and friendly and rude and experimental and conventional. I just wanted to try to be who I am."

It's not difficult to see why Ofili would find disorienting his rapid elevation to feted artist. But he is heading back to England in good spirits, not obviously anxious at the prospect of reimmersing himself into the full glare of the art world. "I don't know if I'll feel the same as I did before... if I'll feel a little bit more comfortable in the role-play or if I'll just be myself. I'm very curious to see."

The exhibition will contain between six and eight paintings that have never been seen, and about a third that have not been displayed in Britain. He is characteristically introspective about the retrospective. "I don't know what the work is going to look like. Some of it could look a little dated." Does he care? He is at such pains to shield himself from what people think, you wonder at times who the paintings are for. "I'm not above it," he says. "I really do care that people are interested in it. I'd like for people to find them interesting and engaging. It would be amazing if lots of people I really respected said, 'These are great pictures.' But then I have to paint it out. I can't care all the time. I'm really driven more by trying to make paintings and the life I might lead in order to do that. The places I might go, the things I might see. That's really exciting."

We are sitting at Las Cuevas on Trinidad's northern coast. "It's like those waves," Ofili says, pointing out to the Caribbean Sea. "It doesn't last for ever. And it shouldn't. It makes its way and then moves a bit of sand and it's gone. That's it. So let's not get too excited. Let's get back out there and find another wave."