The Flitwick Leisure Centre in Steppingley Road will include a dance studio, changing rooms and a 120-station gym.
It will be built on football pitches next to the current centre, which will be replaced with 72 homes after outline planning permission was also granted.
The job was originally estimated to cost £9m-£11m to build and attracted bids from Barr, Heron Brothers from Northern Ireland, and Willmott Dixon.
But SDC secured the project with a £13.4m bid.
Preliminary work started at the end of last week
