The contractor won the job after a four-way single-stage design and building tender process involving McAlpine, Galliford Try and Shepherd Construction.
The new space will be used by Manchester School of Art, which provides a range of undergraduate and postgraduate art, design, media and architectural courses.
To make way for the new state of the art building, a 1970s structure on the corner of Cavendish Street and Higher Chatham Street was recently demolished.
The adjoining Chatham Tower will be retained and refurbished, and connected to a new adjacent seven-storey gallery.
The old structure will be clad in black horizontal stripes set against a vertical finish, resulting in a striking monochrome building. The work is due to complete in summer 2012.
Jim Morgan, Morgan Sindall area director for Manchester says: “This is a hugely significant project for the university and we’re delighted to be working with the Manchester Metropolitan team again.”