Plans for the domed complex have just been approved by Cambridge Council.
The £16m first phase will comprise the main sports hall, a weights room, five squash courts and a fitness suite, while a swimming pool and tennis hall will follow.
The University is providing a loan of £10m to the Sports Syndicate, the body responsible for building the centre.
A further £5m is to be raised by donations to the University Development Office, and £1m is to be generated by the sale of Fenners Building which houses the offices of the PE Department and University gym.
There are plans to raise further money in future years for a 50m pool and indoor tennis courts.