In a drab backstreet in Jette, one of Brussels’ bleaker suburbs, stands the terraced house where René Magritte painted the greatest pictures of the surrealist age. In the ground floor flat of this modest hideaway, which he rented with his wife Georgette, he toiled away for 24 years, from 1930 to 1954, from his early thirties to his mid-fifties, until he finally hit the big time. How wonderful to find this fount of fantasy and creativity in such a workaday backwater, a world away from the bohemia of romantic myth.

Magritte’s humdrum lifestyle epitomises the discreet charm of Belgian Surrealism, so different from its didactic French counterpart. Dressed in a smart and sober suit and tie (which he wore even at his easel) he looked more like a bank clerk than an artist. Yet in a corner of this cramped apartment (now an atmospheric museum) he created a huge range of dreamlike images, whose strange magic still endures.

In 1924, in Paris, André Breton published his Surrealist Manifesto, the bible of a new artistic movement, “free from the exercise of reason and every aesthetic or moral preoccupation.” But although Surrealism first bloomed in France, the place where it took root was Belgium, and throughout this year those enigmatic Belgians are marking this centenary with numerous exhibitions, including several here in Brussels, the capital of Surrealism.

In Brussels, Surrealism is everywhere — not only in its galleries, but in its bars and cafes, in its restaurants and bookshops, and even in the murals on its gable walls. With its chaotic confluence of languages, its collision of modern and antique architecture, this ugly, intriguing city exudes an air of unreality — a disorientating dreamscape, like the setting for a film noir.

Magritte spent three years in Paris with Breton, but he did his best work after he returned to Brussels and moved into that nondescript little house in Jette. Unlike Breton (a dedicated communist), he didn’t want to change the world. His only real interest was the world inside his head.

Magritte’s surrealist countryman, Paul Delvaux, led a similarly quiet, conventional life. His somnambulist murals are scattered all over Brussels, and last month he was the (posthumous) guest of honour at BRAFA, Brussels’ prestigious annual art fair. He made his home in St Idelsbad, a small seaside town on the Belgian coast, a popular retirement resort for bourgeois Belgians (the Paul Delvaux Museum in St Idesbald, has a splendid collection of his surrealist work).

Magritte and Delvaux are among the star attractions at Histoire de ne pas rire — Surrealism in Belgium, at Bozar, Brussels’ Art Deco arts centre. Built by the great Belgian architect Victor Horta (most famous as a pioneer of Art Nouveau), the building is an artwork in itself, and this exhibition is a treat, with lots of undiscovered gems amongst the greatest hits.

The revelation of this lively show is the work of Paul Nougé, the poet and philosopher of Belgian Surrealism, who fulfilled a similar role in Belgium as André Breton in France. Nougé was more lyrical than Breton, not so dry or academic. He was also a fine photographer. His photos of Magritte and his surrealist pals horsing around in Magritte’s apartment seem incredibly modern. It’s hard to believe they were taken a century ago.

Around the corner, at the Royal Museum of Fine Arts, is a parallel exhibition: Imagine! 100 Years of International Surrealism. This eclectic display shows how Surrealism spread beyond France and Belgium, inspiring all sorts of artists who had no direct connection with the movement (as Nougé observed, Surrealism is not a doctrine but an attitude, a state of mind).

The most interesting artists in this display are the Belgians who anticipated Surrealism: Fernand Khnopff, Félicien Rops and above all Léon Spilliaert, whose nocturnal studies of the Ostend seafront look like illustrations from a murder mystery. However the roots of Belgian Surrealism actually run even deeper, right back to the so-called Flemish Primitives, 500 years ago. Upstairs, in the permanent collection, you can see the grotesque visions of Hieronymus Bosch and Pieter Bruegel’s nightmarish masterpiece, “The Fall of Icarus”, a painting with all the otherworldly power of Delvaux or Magritte.

So what is it about Belgium which makes it a mecca of surrealist art? I reckon it has a lot to do with its turbulent history. This damp corner of the continent has been invaded so many times, a battlefield for countless foreign armies, that the Belgians have learnt to keep their heads down and develop their own private netherworlds, free from the dictates of occupying tyrannies.

The conventional notion is that Surrealism died out, eclipsed after the Second World War by Abstract Expressionism. Although there’s some truth in this, it’s really only half the story: Magritte only became famous in the 1950s and painted some of his finest paintings in the 1960s; Delvaux carried on painting masterpieces right up to his death, in 1994 at the grand old age of 96.

Although there are few artists working today in a style which we would recognise as surrealist in the classic sense, the influence of Surrealism has become ubiquitous — not only in the artworld (in the paintings of Anselm Kiefer, for instance) but in every other artform, especially comic books and graphic novels (a genre uniquely bountiful in Belgium — in a country with no common language, pictures are more powerful than words). In its recognition of the subliminal — the realisation that our lives are driven by forces we are unaware of — it was channelled into art the ideas of Sigmund Freud.

I ended up in the Magritte Museum, a palatial building on the Place Royale. It’s dark inside, like a cinema, and as you wander through its twilit corridors these hypnotic pictures come alive. The walls are decorated with quotations, things Magritte said about art and life. “Entre surréaliste, c’est bannir de l’esprit le «déjà vu» et rechercher le pas encore vu,” reads one of them. “To be a surrealist is to banish the idea of ‘déjà vu’ and seek out that which is not yet seen.” For me, it’s a saying that sums up what makes surrealist art so special, and why its appeal is enduring. It’s a window on our shared subconscious, a gateway to another world.

• Histoire de ne pas rire – Surrealism in Belgium is at Bozar, Brussels (www.bozar.be), until 16th June. Imagine! 100 Years of International Surrealism is at the Royal Museum of Fine Arts of Belgium (www.fine-arts-museum.be) until 21st July.