Reader, I'm in love. Smitten. Usual signs – cold sweats, inexplicable exhilaration, inability to sleep. It's art I'm talking about. Art smote me.

The best exhibition by a contemporary artist I've seen in years. Grayson Perry's The Tomb of the Unknown Craftsman at the British Museum. Why the British Museum? Because the show doesn't just feature new work by Grayson Perry, but is also an exhibition of museum artefacts curated by him – the famous artist of the here and now and unknown artists from all ages and all places in a conversation which is so engrossing that you feel you are a thing of unfamiliar thoughts and sensations spinning through time, understanding and seeing as you have never understood or seen before.

But let's not get too grand. "Do not look too hard for meaning here," Grayson Perry himself warns by way of introduction to the show. "I am not a historian. I am an artist. That is all you need to know." A nod to Keats. "Beauty is truth, truth beauty – that is all / Ye know on earth, and all ye need to know."

Both statements succeed in being simultaneously modest and magniloquent, pretending to be shy of meaning as historians and philosophers understand it, while asserting the power of art to access deeper truths than are available to either. Which is fine by me.

"I am an artist." That can sound like swagger or it can sound like apology. Grayson Perry is too intelligent to swagger and has always cast an ironic eye on artistic pretension. "Wildness can be overrated in an artist," he surprised everybody by saying in a speech opening the exhibition. Better to "be reliable and nice to get on with". And what can be wilder at a contemporary art show than a word in support of reliability and niceness?

One doesn't think of him as tame. True, he hadn't, on this occasion, come out dressed as Claire, that formidably muscular Alice in Wonderland alter ego with ribbons in her hair and a dolly nestling into her Adam's apple who has always frightened the living daylights out of me, not because Grayson Perry isn't pretty as a little girl but because he is. Nonetheless, a red leather heraldic tabard and knickerbocker suit worn over a pink chiffon blouse and empurpled tights (being a dark suit and tie man myself I make no claim for the accuracy of this description when it comes to colours or materials) is not what an artist wears when he wishes to be self-effacing.

Though I suspect he wouldn't care to call himself a performance artist – it was as a potter who changed our expectations of a pot that he won the Turner Prize in 2003, don't forget – he more overtly than most artists makes himself, his history, his tastes, his private mythology, the centre of his work. Invoke an artist such as Tracey Emin and there is at once a distinction to be made. The self with which Grayson Perry works is not the self of accidental biography or sentimental mishap. Even Claire, whatever her psychic origins, has stepped beyond individual psychosis into intellectual challenge.

When Grayson Perry walks into a room with rouge on his cheeks and stubble on his chin you feel the usual categories of gender and age, propriety and good form, dissolve. I don't say he dresses to be instructive, but he gives off seriousness of purpose even when he appears to be having fun. And so it is with this stupendous show. It might be billed as a "pilgrimage to his imaginary world" but that's not imaginary as in solipsistic daydream or fantasy – though fantasy certainly figures – it's imaginary as Coleridge described the imagination: an intellectual faculty possessing the power to dissolve, diffuse, dissipate, in order to create, idealise and unify.

It's hard to do justice to any one aspect of this enormously ambitious exhibition without feeling you have failed another. It is permeated with thought – nutting out questions of individual creativity and continuity, meaning and spirituality (he is watchful of "spirituality" as he is watchful of that dire cliché the "journey" of inner discovery), relics and mysticism, belief and magic (he is not a scorner of belief) – but it is also a show of great physical presence and sensuality. I have always liked the pots with which Grayson Perry first made his name; not unravished brides of ceramic quietness, but quite the opposite – great gilded urns and amphorae, beautiful in the ugliness of their satiric and deliberately disquieting decorativeness.

There is no shortage of these in this show, but there is sculpture of a different sort, too: a bronze head of a fallen giant which at first glance could be as ancient as the shamanic forms it memorialises; a glazed ceramic tomb guardian that harks back to the obscene Sheela-na-gigs found decorating Norman and Romanesque churches in Celtic Britain; a flask that could for all the world be from the Rhineland, circa 1500, until you see that the surface is encrusted with aeroplanes. And that's to say nothing of the beautifully fashioned modern-day pilgrim, weighed down with the detritus of our times, and the star piece, The Tomb of the Unknown Craftsman itself, a cast-iron ship, looking weather-beaten, freighted with all that matters of then and now for the journey into God knows where.

Of craftsmanship itself – "a long and sympathetic hands-on relationship with materials ... a relaxed, humble, ever curious love of stuff" – Perry has a lot to say. But it's not only by his eloquence that he refutes the icy, touch-me-not, death-in-life which is conceptualism; the entire show vindicates not only warm "doing" but the ways that the present is bound in reverence to the past by the beauty and boldness of what's been "done".

I confess I feared that the incorporation of Grayson Perry's teddy bear Measles would lead him into whimsicality. In fact, Measles triumphs as the hero of this bold colloquium, appearing now as a household deity, now as the Egyptian god Bes, now as a "guru of doubt" (his best guise, for my money), a protean figure that binds the artist's deepest anxieties to those of the unnamed craftsmen without whom, as this show demonstrates, we wouldn't possess the imaginative wherewithal to comprehend ourselves at all.

Here is not just art but the reason why art is. Miss it at your peril.