It has been designed by Zaha Hadid, who may be consulted again as some of the final details could be changed.
ODA chairman John Armitt said: "You are designing as you build, this is all very normal."
The centre's two 50-metre swimming pools and diving pool will be made available for public use after the games, to be managed by the local Newham Council.
Newham Mayor Sir Robin Wales said: "We want a massive legacy for our population.
"We want more for our people - I want to make it the best possible Games for local people."
But Olympics minister Tessa Jowell said: "They know what they want but we have to make sure there is money to pay for it."
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