The MTMC delivers crucial pre-deployment training for 12,500 personnel every year and has recently trained a battlegroup heading out to Afghanistan on Operation Toral.
The project includes the refurbishment of some of the existing buildings at Bassingbourn Barracks, including accommodation blocks, social facilities, offices, classrooms and training areas.
The existing medical and dental centres will also be refurbished together with the construction of two new training facilities.
The works are part of Project Hercules and follows on from the first phase of work to bring the barracks back into use by the British Army.
Mark Dady, Managing Director of Kier Regional Building Eastern, said work would start this month and complete in summer 2021.