Chelsea is big, ambitious, and has so far cost around £65m - £25m on the rebuilding, the rest on buying the site. It is nothing less than the complete re-making of this famous art school. Previously scattered around four locations, it has now all been brought together on Atterbury Street, facing Tate Britain's new western entrance. It is a bold move by this key member of the London-wide confederation of art schools now called the University of the Arts. Because the gaggles of boho art students who now swarm out of Pimlico subway station lugging their A1 portfolios are heading for a place which was, until not so long ago, an army medical college.

This is high Edwardian redbrick-and-pale-stone architecture. Solid. Enduring. The face of empire, originally designed by the Royal Engineers for the newly founded Royal Army Medical Corps. Here buildings are arranged around an enormous square, fenced off for years, the dimensions of which tell you it was originally a parade ground. Of the three buildings around the square, two were barracks and one was the training centre. Other, later, buildings turn the corner to face the Thames. The one-time Commander's house on the corner - which was later the London pad of Sir Geoffrey Howe when he was Chancellor of the Exchequer - now contains the offices of the college's head, Professor Roger Wilson. Because of its history, the original buildings send out mixed messages. Hang on, am I in a hospital or a college or a military establishment? The answer is: all three.

There is a sumptuous panelled ballroom which the students are eyeing up for installations. A wonderful original library, now vastly extended up on the rooftops. There are all kinds of interesting nooks and corners and spaces, inside and out. It's a smart move by Chelsea because, as Wilson points out, it's all there for the students to colonise and exploit. They're already painting in the corridors and stairwells. The textiles department is up in the attics, the rows of looms eerily reminiscent of 19th century mills. The kilns are down in the basements. Expect the sculpture students to spill out into the parade ground any day now.

This sprawling complex - built, like the old Tate itself, on the site of the vast 19th century prison known as the Millbank Penitentiary - has been stitched together by architects Allies and Morrison with subtle, sometimes almost invisible, extensions and additions. Bob Allies and Graham Morrison have built themselves a mighty design business - in size terms they are far and away the most successful of the generation of bright and bushy-tailed architects who emerged in the 1980s as an antidote to the prevailing orthodoxy of postmodernism.

They have done well by staying out of the limelight. Allies and Morrison are not interested in doing icon buildings, and say so. They believe in well-tempered, cleanly-detailed, understated architecture, and are as happy with conservation and restoration work as they are with new stuff. For instance: it is they who have designed the mega-refurbishment of the Royal Festival Hall, just getting under way now. They are also, coincidentally, building a huge new commercial development behind Tate Modern.

Opponents of the Allies and Morrison approach (who tend to be the more flamboyant architects of their generation) say that they are dull, their buildings boring, their formula predictable. This is unfair not because it is wholly untrue - their buildings can certainly be forgettable in that Polite Modern way - but because it is absolutely deliberate. Allies and Morrison do not do cynical architecture, they do functional and often elegant architecture that is a considerable cut above the bog standard. They are principled pragmatists. Last summer the profession was polarized when Graham Morrison came out fighting in a lecture, castigating the iconographers and defending his brand of no-signature, no-nonsense architecture. The shock was palpable. The affair recalls what a former Labour party chancellor, Denis Healey, once said after an attack by his rival Geoffrey Howe: it was like being mauled by a dead sheep. Morrison, in contrast, turned out to be a wolf beneath the wool.

And the new Chelsea College, for my money, shows the pragmatists on top of their game. Allies and Morrison partner Paul Appleton, whose baby it is, has worked the old buildings assiduously, revealing their merits and freeing up their interiors by grafting on additions in glass, timber, brick, even a slate-like fibreboard. A complete new square building, known as the "casket" has been dropped into a space at the heart of the complex and fits its hole so snugly that at first you are scarcely aware it is there. Clad in translucent panels, it bring daylight softly into the studios, and glows gently at night.

A tall narrow atrium, crossed by walkways, is the entrance to the college, with refectory and bar leading off it. It's a bustling, lively place. Another set of studios fills in a left-over triangle of land in a razor-sharp three-cornered building. After all this careful mending, it's a bit surprising to find some rather prominent new additions, in gleaming metal cladding, around the back on the western side. What can the well-heeled Pimlico neighbours think of this eruption of modernity?

Needless to say, student programmes are being drawn up in collaboration with the Tate. The biggest idea here is not architectural, but social. After all those years of splendid isolation down on its Pimlico plinth, Tate Britain now finds itself with thousands of art students right next door, all cheerfully ready to swarm all over it. They moved in a fortnight ago. Already the whole area is coming alive. It's true, you don't always need signature architecture. You just need clever thinking.

www.alliesandmorrison.co.uk - check out the architectural pragmatists.