Firstly, the firm has will refurbish the Engineering Building at the University’s main Woodhouse campus under a £22.5m deal.
The project involves refurbishing levels three, four and five of the 1960s building, as well as completing the maintenance backlog on the remainder of the building.
It will also undertake the £15.3m refurbishment of the Grade II listed Edward Boyle Library.
The scheme, which encompasses all six floors of the 1970s building, includes fully refurbishing the study areas and replacing the engineering systems and roof.
Greg Fitzgerald, executive chairman of Galliford Try said: “The strategy for our construction business is based on long-term relationships with respected clients and these two contracts are an excellent example of that approach.”