The job involves a mix of restoration, alterations and new buildings, working with both new-build and existing listed buildings.
Morgan Sindall will demolish the Examinations Halls Building to provide a major new building in its place and refurbish the Grade 2 listed Arts School and ground floor of the Old Cavendish Labs (East and Raleigh Wings).
Work is expected to start before the end of the year on the project which will cost an estimated £39m including demolition.
It is architect Bennetts Associates first job for the University.