The new building, called Home and designed by Mecanoo Architects, will house the Cornerhouse gallery and theatre and the Library Theatre Company in Manchester.
Construction is set to start this month for completion in 2014.
The structure will incorporate three existing viaduct arches that will house the venue’s education rooms. There will also be a 500-seat theatre, a studio, a gallery and a five-screen cinema.
The project forms part of an £80m programme at First Street North, which will also see a new hotel, multi-storey car park and restaurant area built around a new public square.
Wates was awarded the work through the North West Construction Hub following its appointment to both the medium and high value Hub frameworks in 2010.