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London University's Imperial College is mighty proud of its new business school building. Which is hardly surprising considering it commissioned the design from Foster and Partners and donated a prime site next to its main entrance, and persuaded one of its better-off former students, Gary Tanaka, to cough up £26m towards the project costs.

The resulting building opened for business last week after an 80-week construction programme by contractor Exterior. In it, Foster's famous elegance is recognisable in the colonnade of slim tubular steel columns fronting Exhibition Road. And behind this frontage stands a curious hybrid of a building. Most of the interior turns out to be empty space, or rather, a spacious atrium rising up six floors to a flat glazed roof. This atrium is shared between the business school and the entire college, for which it serves as a grand entrance-cum-exhibition hall. Within the atrium stands a gleaming silvery drum housing most of the business school's teaching spaces; the buildings overlooking it on three sides have been refurbished for college departments.

Inside the shiny drum, six round lecture theatres, three with semi-circular and three with horseshoe layouts, are stacked on top of each other. As pioneered in the early 19th century by anatomy auditoriums in medical schools, the horseshoe-shaped auditoriums look and function like debating chambers for students and staff. On its outside, the drum is sheathed in an armour of narrow, horizontal, stainless steel tubes, which act as acoustic baffles; the gaps between them serve as vents.

On the other side of the atrium stands the pre-existing Black Tower. Its archetypal 1960s facade of strip windows and black spandrel panels has been updated to the 21st century in Foster style with an overcladding of slanted louvres in frosted glass.

The atrium itself is roofed over in translucent pillows of ETFE membrane, which admit daylight without letting heat escape. Measuring 4 × 21 m each, they are claimed to be the largest ETFE pillows ever produced, and are fitted with an innovative system of electric filaments. If triggered by a fire, the elements burn and evaporate the membranes to allow smoke to escape.

The building works have been carried out in a design-and-build contract by Exterior. "This has been the college's first project to adopt a collaborative approach," explains John Walsh, the assistant estates director, "and we chose Exterior because they demonstrated collaborative thinking. We went for design and build in pursuance of cost certainty." As part of this approach, Foster and Partners and the other consultants were novated to Exterior by the college's estates division. The college's project manager, Nick Mather of Gardiner & Theobald Management Services, confirms that the building was completed on time and to budget.

The Foster glamour has not come as an afterthought to the business school. At the start of the project, Tanaka said his aim was to create "a bit of Broadway and glitz to attract good academic people". The message was brought home by the college's rector, Sir Richard Sykes, at the topping out last May. After promising that the building will give the college "some grandeur", he drew parallels with the area's best known architectural project, Joseph Paxton's glass hall for the Great Exhibition of 1851: "The drum of amphitheatres and these columns will gleam, and the Crystal Palace will return to South Kensington," he proclaimed.