Peter Doig on his new Edinburgh exhibition

The exhibition, Peter Doig: No Foreign Lands, showcases works created during the past ten years. Picture: Jane Barlow

In the midst of all of this is Doig himself, an island of stillness, standing, looking, in front of a painting which has just arrived from MoMA in New York. He moves in close and looks a bit more. “I forget how I make things,” he says, quietly. “This is an opportunity to look at paintings, just reflect on them, to make connections between things.” He gives a wry half-smile. “It would be great to be able to buy a few of your own works.”

Doig, 54, is tall, athletic and speaks with a soft North American burr (much of his youth was spent in Canada). In a rare effusive moment, he exclaims over the “magnificent rooms” of the former RSA building – “Some of the best rooms in the British Isles for paintings.” He is slightly bemused by the fuss: his show is a major coup for National Galleries of Scotland and the press is lined up to interview him.

In the past decade, Doig has entered the big league. He had long been respected, critically acclaimed, credited with making painting fresh in an era of conceptual cool. Art students loved him. He was shortlisted for the Turner Prize in 1994. But he wasn’t a celebrity until one of his paintings sold at auction for £5.7m in 2007, four times its expected price. A 25-year retrospective at Tate Britain in 2008 – his first ever one-man museum show in Britain – helped cement his reputation. Now a new painting can fetch over £1 million.

Doig has always been hard to pin down, a painter without borders. He was born in Edinburgh – and remembers many summer holidays spent with his grandparents in Lower Dublin Street – but his childhood was in Trinidad and Canada. His family moved frequently: he went to nine different schools, studied art in London, and now divides his time between Trinidad, New York and Germany, where he has a teaching post.

“When I’m in Canada, I’m considered British. When I’m in Scotland I’m considered to be a Yank. When I moved to London I was considered American. I’m always foreign. In Trinidad I’m certainly foreign.” He shrugs. “But then who’s from where?”

No Foreign Lands, the title of the exhibition, comes from Robert Louis Stevenson’s The Silverado Squatters: “There are no foreign lands. It is the traveller only who is foreign.” Doig has painted both Canada and Trinidad, but his paintings have the quality of dream or memory, as if we were separated from each place by a veil of strangeness. They strike a chord in a world which is connected by international travel, yet leaves many people feeling like strangers.

We look at a lush, green landscape of Trinidad. His paintings, he says, are more about “atmosphere and spectacle” than the place itself. This show focuses on his work since moving with his wife and five children to Trinidad in 2002. But the country in them is a country of the mind. “My Trinidad paintings are questioning what permission there is for me to make them. It’s a complicated place, a post-colonial society. I am a foreigner. People are very proud, very aware of their culture.”

Many of the paintings in the show have a similar mysterious quality. There’s a little girl up a tree – his daughter, he says – but impossibly far up, gazing down at all. There is an ethereal picture of man dressed as a bat, inspired by a character from a Trinidad masquerade. Some pictures are overtly foreboding, others have only the slightest hint that all is not well. The paint itself adds to the strangeness. Doig is a painter of great technical facility. As one critic wrote, he “never lets you forget the strangeness of picturing itself”.

He almost laughs at “this ridiculous canoe” which runs end to end over a canvas at least three metres long. He found it on an album cover for blues-rock band The Allman Brothers and got rid of the band, leaving only the Messianic-looking bass player, the late Berry Oakley. Canoes feature frequently in Doig’s painting, resonant perhaps with the sense of wanderlust, though they are drifting, not travelling, and always on water with untold depths.

Doig works with found images, photographs, postcards, fragments of advertising, snaps of his family, bringing ideas together in an associative way. Often he will start a picture and wait for years for an image which might complete it. “You get stuck and you leave something. But being stuck doesn’t mean it’s a disaster, it just means you’re stuck. I always have a lot of things on the go.” And often he doesn’t finish them until he has to. For this show, he worked 20-hour days in his New York studio to meet the deadline.

Doig had no childhood ambition to be an artist, but did a foundation course at Wimbledon College of Art in his twenties and got into Central Saint Martins. He had left home in his teens and worked on drilling rigs in the prairies of Western Canada. “I had no self-confidence, I didn’t think I was good enough to be a painter. But at art school I became interested in painting and painters. I developed painting ability somehow. I used to do a lot of painting and decorating,” he smiles. “It’s hours and hours of work with a brush. I think you gain a level of control.”

Despite his modesty, Doig’s work has been talked about in relation to Matisse, Monet, Turner, Delacroix, Gauguin, all with some justification. “I still think there’s a lot to be learned from looking at paintings from the past. There was a tendency in the 20th century to always be trying to be the next step in what painting could be, what art could be. Now you can follow these different avenues a bit more. That to me is what makes being a painter compulsive.”

He was painting in London in the YBA years when many a pundit was prepared to declare that painting was dead. “I heard that, but never paid any attention to it,” says Doig, mildly. “Painting was what I liked doing, what friends of mine did, what we liked talking about. I never put painting on a pedestal, there has always been lots of terrible painting being made.”

He first came to the notice of the art world with his large-scale Canadian landscapes, atmospheric, empty, sometimes beautiful. He mashed memories and tourist brochure images and hit on a style which was his own. “The advice I would give to younger artists is work within what you know, then you’re not going to be criticised for following someone else.”

He distances himself from the hype, from the sales figures. “It’s all about the market. I didn’t orchestrate this and neither did any of the people who represent me. I think you can’t help feeling some sort of pressure, but you have to ignore that side of success, otherwise you would never develop. You have to put the blinkers on.”

He does think one day he might paint Scotland. He was on holiday in Mull last year and took lots of photographs. One of the new paintings in the exhibition shows his youngest son in “a boat which becomes a raft” floating towards an island. “It’s not a painting of Mull but it reminds me a Scottish island, it doesn’t look like Trinidad.”

He rejects the notion of the romantic, though his paintings can be that and more. He is more comfortable with the sense that his work is uncomfortable, unsettling. “You want to make paintings that have got some sort of tension in them. I don’t want to make paintings that are about settling people down.”

• Peter Doig: No Foreign Lands is at the Scottish National Gallery until 3 November, www.edinburghartfestival.com