Sir Steve joined International Olympic Committee member Sam Ramsamy to cut the ribbon at the ceremony in Mayesbrook Park.
The former rower met pupils from Barking Abbey School, All Saints Catholic School and Trinity School during his tour of the £8 million SportHouse.
The pair also opened the park’s refurbished athletics arena.
Sir Steve is best known for winning gold medals at five consecutive Olympic Games. He said: “I got involved in the Olympic bid because of things like this – making a change to the community at grass roots level.
“With world-class athletes training here, it inspires others.
“Viewing all these superb facilities, it just goes to prove what a fantastic, lasting legacy the Games will bring us all.”
At 5,000 square metres – the size of 54 badminton courts – SportHouse is Britain’s largest sports hall. It will be used for practice by competitors in Olympic handball, Paralympic judo and wheelchair rugby.
A £2 million makeover has transformed the old athletics arena, with an Olympic-standard track, long and triple jump pits and new changing rooms.
Olympic athletes getting ready for the Games will be able to use the track.
And local people can sign up to use the facilities at SportHouse, including its well-equipped gym.