The firm beat rivals Graham, McLaughlin & Harvey and local firm Ashe Construction with a £20m bid for the project, which was initially budgeted to cost £25m.
Architect NORR drew up designs for the new three-storey building at the heart of the campus, located in Brookmans Park.
Works will involve demolition of the majority of the existing main clinical block and reprovision of office and research space.
The demolition will leave the CEEED exotic disease building in place.
R G Carter will build the 70,0000 sq ft hub that will connect to two existing modern buildings.
The building will include a 430 seat lecture theatre, teaching spaces, library, category 2 research laboratories and staff offices.
Consultant AECOM is mechanical and electrical engineer and Conisbee structural engineer on the project.
