The Olympia Leisure Centre will be built within the West stand of the new Windsor Park stadium development and replace an existing facility.
The development includes a main pool and a learner pool as well as a cafe, health and fitness suite, sports hall and multi-purpose rooms.
Director of parks and leisure services at Belfast City Council, Andrew Hassard, said: “We welcome the award of the planning approval for the new Olympia Leisure Centre and will continue to work with the IFA, DCAL and Linfield FC to develop the project, as part of our £105m investment to transform leisure across the city.
“Many of our centres are getting older and we’re making plans to improve our leisure facilities and services as part of a wider investment to improve the health and quality of life of our citizens, including those who join us under Local Government Reform. These plans are in addition to our previously announced £150m investment programme for the city.”