The centre was funded by Jonathan Sorrell, an influential designer and millionaire, and the Department for Education and Skills, which has contributed pound;1.75million over three years. Mr Sorrell, chairman of the Commission for Architecture and the Built Environment, said he did not believe any new schools should be built unless their plans had been approved by pupils.
"It should be mandatory to have them involved," he said. "When you do, you get results beyond your wildest dreams. Making pupils the client is absolutely the best way because they are on the front line. They have incredibly strong views and insights."
The exhibition will feature pupils' 12 most common complaints about schools, including unsafe toilets, lack of social space and poor dining facilities.
The centre will hold workshops over the next three years to research what young people want.
It grew out of a scheme started seven years ago, which paired schools with influential designers such as Paul Smith, who designed the uniform for Aldercar college in Nottingham.
At Acland Burghley school in north London, pupils consulted with designers on replacing their out-of-date canteen with an internet cafe and outdoor dining areas.
Mr Sorrell said he hoped the centre's approach to pupil involvement would be mirrored by local authorities.