The contract was awarded by main contractor Wates and work on the building envelope is due to start on site in January 2014.
The new venue will provide a home for the recently-merged Cornerhouse and Library Theatre Company, and will include a theatre, cinema screens, gallery space and digital production facilities as well as bars and restaurants.
鈥淭his flagship building will provide a cultural centrepiece within an area that is undergoing an exciting transformation and we鈥檙e proud to be involved,鈥� said Prater business development director Andy Newman.
The building is designed by Mecanoo Architects.