The first of five "AdiZones" was the brainchild of The Great Outdoor Gym Company, which designed and built the area at Tower Hamlets.
Georgie Tarrant, managing director of the firm in south London, said: "The AdiZone is designed to break down barriers to physical activity.
"Many people simply cannot afford the gym or access to sports facilities and the zones bring fitness spaces to the heart of the community."
The project for Adidas, official sportswear partner for the London 2012 Olympic and Paralympic Games, includes kit for pull-ups, leg and chest exercises.
The other four zones, due to be built in Greenwich, Hackney, Newham and Waltham Forest, will include tennis kit, climbing walls, ski machines and abdominal benches.
Christine Ohuruogu, 400m Olympic gold medallist in Beijing, opened the new 625sq m site at Wennington Gardens last week.
Nick Craggs, a marketing director for Adidas, said: "AdiZones will be free to use as part of our pledge to create a legacy from the London 2012 Games."
The fitness areas will be built on disused or run-down land. "AdiZone activators" will work with local schools and sports clubs, and coaches will be encouraged to visit to spot talent.
The London boroughs will maintain the zones and Adidas hopes that its initial investment will prompt Government funds.