Work was due to begin at the start of this year but the start was put back by the University for a spending review.
The 180,000 sq ft complex, which will be built on a sports pitch on the western edge of the Broomhill campus, gained planning in 2017.
Kier is presently selecting a groundwork contractor to start the project, which has been designed by HLM Architects, with Arup as M&E consultant and Mott MacDonald providing structural engineering.
The two-year project is expected to cost around £50m to build uniting three departments – economics, politics and sociology – as a ‘hub’ under one roof.
Currently the Social Sciences estate is spread across 19 different buildings across campus.