MY afternoon with David Shrigley starts with a story about a bass guitar. Or, more precisely, about a printmaker in Copenhagen who buys a motorbike without telling his wife, who retaliates by secretly buying a dog, which in turn eats a shoe it finds lying around the house - a shoe that belongs to David Shrigley. The guitar was a present, the printmaker's way of saying sorry. It now sits propped against a sofa in an airy top-floor room in Shrigley's house in Glasgow's west end.

"So," grins the Englishman, as the tale corkscrews to its finale, "I got this really beautiful bass guitar because a dog ate my shoe." If the enormous white Birkenstock sandals he wore to answer the door are anything to go by, that shoe was the canine equivalent of a supersized Happy Meal.

David Shrigley's core activity is art, of course, not music, which is why he was in Copenhagen working with a printmaker. But the story is relevant because in both it and his work you find the same refreshing proposition: that the world is strange and absurd, a place where a dog eating a shoe in Denmark can bag a 39-year-old artist in Glasgow a shiny new bass guitar. Or, to use the title of one of Shrigley's own books, where ants have sex in your beer.

The writer Will Self, a longtime fan of Shrigley's, has his own Selfish view on how to define this Shrigleyesque world: it is a place, he once wrote, where "giant cantankerous dogs roam the land refusing to let you use their deodorant sticks".

It's only lunchtime, but Shrigley's day has already been filled with activity. He started with a strenuous early-morning yoga class and, when I arrive, has just concluded a meeting with two representatives of Gateshead's Baltic Centre for Contemporary Art. They have travelled north to record a podcast ahead of an exhibition of new work which opens there this week. Called simply David Shrigley, it will be the Macclesfield-born artist's biggest British show to date.

On the floor by Shrigley's feet when we sit down to talk is a piece from the exhibition. It's a wall clock with the hands removed and a plastic leg bone attached in their place. Shrigley bought the clock on the internet and it arrived the previous day. "It's really hard to buy heavy-duty clock mechanisms," he muses, before adding "not that one tries very often." He hasn't had time to rig it up properly, and still can't decide if the leg bone should replace the hour or the minute hand. I think about suggesting he call it Femur Fugit, but resist the impulse.

Illustrator, cartoonist, animator, conceptual artist; ironist, humorist, absurdist. Shrigley doesn't really mind what title or category people want to use to describe him. He has no fear of being pigeonholed: in fact he quite likes pigeons, returning to them often in the drawings that have graced gallery walls, books and, for three years now, the pages of The Guardian's Saturday magazine. For his Baltic show, however, he is moving beyond the two-dimensional.

"I was going to show some drawings but I think it's an opportunity to use the space. In the past I feel I haven't always used the space I've had to the best advantage by trying to use drawings, because that's my signature. So for this show I've tried to make work that is very integrated and large and which uses the space properly."

To that end he is working on a series of sculptural works, of which the bone clock is but one. Another is a four and a half-foot-high pair of fishing waders with wellies attached. They've been filled with plastic foam that spills over the top like a frothing head of beer. The piece is called Cheers.

Although drawing is Shrigley's signature medium, he regularly leaves it behind for periods of time. In part that's because he wants to rise to the challenge of making site-specific work, such as for the Baltic show. But it's also down to a restless nature and an awareness that it's not always healthy to turn out leaf after leaf of tree-splittingly strange drawings.

"It's a very insular, very introverted activity," he says. "You can go a bit nuts after a while, just sitting there drawing all day and listening to The Fall. Quite often when I'm making a series of drawings, it'll take a month and I'll realise that I've not spoken to anybody all day."

There will be some drawings in the Baltic show, however, if only because the gallery has walls on which to fix them - and because the visiting public will expect to see them. But it's the sculptural pieces that seem to have taken his fancy now. He's even thinking about giving up the Guardian cartoon.

"I've stopped buying the paper on a Saturday. I used to keep all the cartoons and I don't any more. I've lost interest a little bit," he says. "Maybe I shouldn't do it any more. But I figure they'll tell me to bugger off pretty soon anyway, so that will make the decision for me."

I figure they won't. I figure he will have to make the decision for himself, because he is that rare thing in the conceptual art world - an artist with a high degree of visibility who is both credible and popular. As well as the Guardian slot, he has made videos for Blur, created the opening title sequence for the film Hallam Foe, made his own sequence of animated short films, recorded an album of spoken-word pieces, published several books of illustrations, designed record covers and, in 2006, the entire programme for the three-day Triptych music festival. Given away free in their thousands, they now go for a tenner on eBay.

More internet-based proof of the artist's cult status can be found on his own website, where he posts photographs of Shrigley tattoos he has been sent. One fan pictured has had "hello" inked onto the nape of her neck in his trademark childish scrawl. Another is pulling aside a top to show a pigeon on her breastbone with the legend "Pathfinder" beneath it. A third has eight lines of script on her arm, complete with crossings out, another trademark. There is a preponderance of women, for some reason, though the hairy forearm showing a long-haired figure climbing a flower next to the word "homosexual" is presumably male.

The original drawing that image is taken from featured in a group show called Laughing In A Foreign Language at London's Hayward Gallery earlier this year. The exhibition featured work by 30 artists from 20 countries and the theme of the show was humour. BBC arts programme The Culture Show sent roving reporter Karl Pilkington - Britain's funniest man, if Ricky Gervais is to be believed - to see if his funny bone was tickled. It wasn't, though Shrigley was game enough to be interviewed about his contribution.

Patently, however, Shrigley's work is funny. How can you not laugh at "interventions" like the note he once pinned to a Glasgow lamp-post that stated: "While you are reading this there is a man in one of the windows high above you who is taking your photograph. He will then make a wee model of you and put it with other wee models of other people. Then he plays weird games with them." Or the recent cartoon in the Guardian that showed a pigeon saying: "I'm off to London to shit on the government."

The interventions have tailed off dramatically over the past decade. Shrigley found he became more interested in the photographs he took to record them than in the act of signposting itself, and that in turn led him along other artistic byways. But the humour has remained, and Shrigley retains a friendship of sorts with his fellow-traveller in those public acts of anonymous urban whimsy, the stencil graffiti artist Banksy.

Banksy, for the uninitiated, spent a decade stealthily spraying his subversive artworks on to walls in London and his native Bristol. He has managed the not inconsiderable feat of gathering a cult following and retaining his anonymity while pocketing thousands of pounds for original artworks. Today he regularly makes the news when an old stencil is painted over or stolen - it does happen - or when a new one springs up, such as the image he sprayed on to Israel's controversial security fence.

So, has Shrigley met Banksy? "I have met Banksy," he says cautiously. "But I'm not sure if I'm allowed to tell anyone I've met Banksy." Maybe you just thought you met Banksy, I suggest. "No, I did meet Banksy. I keep in touch with him. I have his phone number."

Like Banksy, Shrigley started out with the intention of cultivating his anonymity. But as the media became interested in his quirky interventions, he saw that it was fanciful to imagine he could keep up the act. "I realised it was far more effort not to do interviews than to do them."

And so he crept slowly into the spotlight from the wings, gradually moving towards centre stage. Today he agrees to most interview requests, works hard, listens to The Fall a lot and turns out a vast quantity of work. As for the "vision" of the world that has caused the word "Shrigleyesque" to enter the lexicon, he accepts that fame sticks to his name like fluff to a jumper but remains a little bemused by it all.

"It's hard to see yourself as the world sees you," he says. "I have people come up to me and say, Well surely you must realise you occupy this position?', and I don't really. I just don't see the work as other people see it. The only thing I do is try to make sure it's good work."

He is nonplussed, too, by the rumours of his own oddness that reach his ears.

"You hear the same thing over and over again, which is that when they meet you people are surprised you are less of an outsider, or more normal and sociable than your art would suggest. It's something that's often said and it's obviously a pertinent point. It's quite a regular thing that people write about me and my work."

After an hour in his company, I'd write it myself if he hadn't already said it. But that disconnection between the work and the character of the man is, in some senses, a relief: it means there is an element of masquerade to the madness.

From a survey of his art alone, the old phrase "Who is he and what does he want with us?" could have been made for David Shrigley. In person, it becomes a cliché that fits him none too well - though better, I imagine, than the shoe that Danish mutt mangled.

David Shrigley opens at the Baltic Centre for Contemporary Art, Gateshead on Wednesday (until November 9)