Willmott Dixon has been given the go-ahead by Westminster Council for its £60m scheme to build a leisure centre and 156 new homes.
The construction firm will demolish the two existing leisure centres and, at one site, will build the new £20m Moberly Sports Centre, complete with swimming pools and sports hall.
At the second site, new homes will be built along with a smaller community sports facility which will include a 3-court sports hall and flexible activity space.
Work is set to start in the autumn and will be completed during 2016.