Everyone seems to know the work of Olafur Eliasson. Just ask them and find out. Did they ever visit that vast shimmering sun in the Tate Modern turbine hall, or see a serpent of green paint unspooling down a river or find a glittering rainbow in some museum gallery? The answer tends to be yes, because this artist, in one sense, is a superb showman. He knows how to pull the punters in.

But where is the brash fairground character? For all that the public may be familiar with his pieces, how many would recognise the 40-year-old artist? The Icelander has joined Björk as his nation's most famous export, his Tate Modern Weather Project attracted an almost cultish following and his dramatic follow-up - four enormous, free-standing waterfalls to be installed in New York harbour - will form part of the Manhattan skyline later this summer.

The waterfalls, to be installed from July at sites including one beneath the Brooklyn Bridge, will reach up to 37m (120ft) high - close to the height of the statue of Liberty - and will be lit up at night. In an interview earlier this year, he said: “It's about seeing water in a different way... A waterfall is not just an iconic phenomenon, it is also free-falling water - in the literal sense but also in the sense that it is freely accessible. In today's world, water is very rarely completely free.”

“My work is not about me, it's about you,” he tells me. It's about the perceptions of the people who participate in his “experiences”. The details of his own biography are not relevant, he insists. He shuns what he sees as “the very British phenomenon of personality fetishism”. He does not want to be turned into a brand like the “Brit-bloody-pack”. And this is hardly surprising when his atmospheric installations double up so nicely as special effects. “We are always nicking his ideas for shows,” a fashion stylist informs me. This week Taschen publishes an encyclopaedic monograph, Studio Olafur Eliasson, and the first major American retrospective of his work opens at the Museum of Modern Art and its hip contemporary outpost P.S.1 in New York.

But Eliasson continues to work calmly in his cavernous Berlin studio, where, with the help of some 40 assistants, plans for anything from the optical illusions created by colour-saturated rooms to designs for a new hydroelectric car, displayed in a freezer and encased in ice, have been dreamt up and developed.

Eliasson doesn't share a modernist obsession with the avant garde. He liked the phenomenal success of his Weather Project because he thinks museums “should be in the middle of society. They should be full and bring people together”. Indeed, the title of his new show is Take Your Time. “So the gallery is going to get even fuller with everyone hanging about.” Visitors don't need to puzzle over the meaning of his work. Their point lies in the experiences they offer.

I came prepared for a struggle. But, fortunately, Eliasson has decided to confute expectations. He starts to talk about his private life. Perhaps it's because it's a Saturday. He used to work round the clock, he tells me. But now he and his Danish art historian wife Marianne (they have been together for ten years) have a family, he has cut his workload by half. “I only do a 40-hour week now,” he laughs.

Today should be home time and, as if to prove the point, a four-year-old runs in to attend to a souped-up red tricycle. His name is Zakarias. And he and his two-year-old sister, Alma, have both been adopted from Ethiopia. That's one of the main reasons why, although Eliasson has worked in Berlin for almost 15 years, his family home is in Copenhagen. “For all Germany's academic and political sophistication, there's a lot of xenophobia. Whereas Denmark has a far greater diversity in a day-to-day sense.” So why doesn't he live there all the time? “Denmark is probably the most frictionless country in the world. Nobody is rubbing your back. Nobody is slapping your face. It can be bloody hard to tell if you are even existing. That's what's so worrying about Scandinavia - that people are all the same and they are not worried about it.”

Eliasson has always resisted setting his work directly in the context of his Icelandic heritage. He may be inspired by his native landscape but his pieces are not reproductions, he insists. And besides, “I don't want to mythologise it. You can barely talk about the Nordic landscape without the Ministry of Culture launching a campaign.”

But, when pressed, he admits: “I say that my work is not about nature, but that's not true, of course. I just don't want to hand out normative tools for people to interpret my pieces.” The truth is that his work is profoundly influenced by his childhood experiences. “Icelanders have a very distinct relationship with their landscape,” he explains.

His upbringing was unspectacular, he assures me, “a classic Icelandic case with a lot of fishermen in the family”. His parents met when they were studying in Denmark, his father to be a cook (though he was always sculpting and painting) and his mother to sew. When Eliasson was a toddler, his parents divorced and his father returned to Iceland. The young Olafur would visit, typically staying with his grandparents.

It was a fairly impoverished childhood, he says, its dullness alleviated by such minor acts of danger and delinquency as retrieving lost golf-balls from a sandbank before the frighteningly strong riptide swept over it, and then spending the long light nights whacking them off the wall of his grandparents' garden to hit the huge oil cylinders in the harbour below. The great hollow rumbles would clash and growl in the mist. “And when we got bored of that we would aim at pretty much anything,” Eliasson says. “There we would be, four or five kids in the middle of the night, aiming at any vehicle that drove by. I got quite good with a seven iron.”

With his father he would go travelling - “because that's what Icelanders do”, he says. “Think camper van, a crate of beer and taking a radio along and not missing the news every f***ing hour. And yet because of their country, Icelanders have a very strong sense of temporality and scale, of distance and height. It's not esoteric or spiritual or particularly existential. It's pretty physical, actually.” But it comes, he suggests, from living in a land where the sun spends half the year only ten degrees above the horizon, casting a low light that illuminates objects from only one side. “This can be very dramatic,” he says. “A little house can become like a castle. And people who live in this twilight zone develop a particular sensitivity to their surroundings.”

This is the sort of physical alertness that Eliasson aims to awaken. Of course his personal sense of it could equally come from his teenage passion for break-dancing, when, dressed in a silver spandex costume whipped up by his mother, he would spend several hours a day spinning wildly in front of a mirror. His crew, apparently, won the Scandinavian break-dancing championship.

Now, in his art, he aims to place this power of physical presence back into the environment from which we have grown so detached. He turns on a switch that sets the vast circular mirror suspended from his roof spinning. Soon horizons are heaving. I feel as if I am standing on deck in a slow Atlantic swell. I can't take gravity for granted. This mirror is a prototype for a piece now installed in New York. It is the sort of work that can help to recalibrate our relationship with reality and, through this refreshed sensitivity, renew our relationship with the world.

But Eliasson isn't tempted into hippy New Age territory. Rather, he believes with a campaigning optimism that art can affect social change. He sets out to instil a sense of responsibility at a fundamental, physical level. “I want my work to take the sensitivity of the mind into the body,” he says. “This is something the TV can't do. It's why the internet is a great mishap. There is no physical exchange.

“How do you feel when you feel something that until then you have only been thinking about? That is what I want to explore. How do you feel with your skin? And what happens when you connect these feelings with questions of a political or ethical nature? If you can do that - and you can do it without being patronising - then you are doing something very exciting,” he says.

Studio Olafur Eliasson is published by Taschen on Friday, rrp £80, and is available from Times Books First for £72, free p&p. Call 0870 1608080 or visit timesonline.co.uk/booksfirst

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