The job to build the pool next to Blackbird Leys Leisure Centre will complete a run of swimming pool building jobs for the firm in Rochdale, St Albans and Lewisham in south London.
The estimated cost of the new pool, designed by Faulkner Browns Architects, is around £9m.
The main part of the project is a 25m, eight-lane swimming pool with moveable floor.
The building will also include a teaching pool and a fun pool which are all due to open in 2012.
The city’s Temple Cowley Pools and Blackbird Leys Pool will close once the new pool is complete, with the Cowley site sold to partly fund the project.