Planning consent from the Royal Borough of Kensington and Chelsea paves the way for contractor Leadbitter to start next month.
Building of the leisure centre will run in parallel with the academy so that both new buildings can open together in 2014.
The proposed new centre will have three pools, a 120 station gym and an eight-court sports hall.
Councillor Sir Merrick Cockell, Leader of the Royal Borough of Kensington and Chelsea, said: “This is a landmark day for the North Kensington community and represents our ongoing commitment to investing in great facilities for our residents.
“Despite the challenging economic climate we are proud to be able to build a new academy and leisure centre which are going to make a vital contribution to local life for decades to come.”