Roberts Limbrick Architects will work alongside Willmott Dixon to create the new complex with two new pools and other leisure facilities on the site of the former Forest Hill Pools.
The existing Victorian frontage of Forest Hill Pools will be retained.
Facilities in the new building will include a 25m pool, a 16.7m learner pool, fitness gym, two studios, community room and a café.
The new development will include facilities and access for those people with disabilities.
Mark Tant, managing director at Willmott Dixon, said: “We’ve done a lot of work in recent years in Lewisham, such as Hither Green Primary School and Crossways Academy, and like those projects, we will aim to ensure our work benefits local businesses as much as possible through the sub contractors we use.”