The planned two new buildings will take the recent investment in the University’s campus to over £150m.
Vinci Construction has scooped the contract to build a new home for its Department of Psychology with a £16.6m bid.
L-shaped building, known as 10 West, will be positioned adjacent to the School of Management on the western part of the University campus.
On the south side of the campus, Bouygues has won the £16.3m job known as 4 East South to build a new faculty of Faculty of Engineering and Architectural Design.
The firms are understood to have beaten Willmott Dixon and Balfour Balfour to the jobs.
Both projects gained planning earlier this month allowing for work to get underway soon.