The firm is expected to start work on the general teaching building next month after edging ahead of rival bids from Miller and Leadbitter.
The new 5-storey building will house two 350-seat tiered lecture theatres and several teaching classrooms.
The university has three other construction projects in its programme. these are:
A £43m student accommodation complex containing 708 bedrooms which is due for completion in summer 2014
A new £10.9m, four-storey Centre for the Arts, with bids due to be called before the end of the year.
Refurbishment of the 1 West complex which will be carried-out in three phases worth a total of £22m, with Cowlin taking the first £6m phase.
University vice chancellor, Prof Dame Glynis Breakwell, said: “Despite continuing economic uncertainty and the changing tuition fee landscape, the University of Bath is facing the future with great confidence.
“Our aim is to further enhance the university’s ability to deliver an outstanding student experience; creating additional facilities for research, and an inspiring working environment, as well as providing cultural and economic benefits for the wider Bath region.”