The builder beat bids from rivals Mansell, ISG and Wates to secure the job, which is the biggest it has won for a year.
The new three-storey police station will accommodate around 200 police officers and staff as well as specialist units including scenes of crime, roads policing, CID and a 16-cell custody suite.
The new station at Beckwith Knowle is due to open next spring and will replace the existing 1930s base in in the town centre, which will be sold to part fund the move.
Balfour Beatty Engineering Services will carry out M& E works on the project.