Medallists Hoy, Ennis, Pendleton and Smith are joined by a number of other athletes from Team GB in their own version of the song.
The athletes are seen out of character, with Ennis air-guitaring with a table-tennis bat, Pendleton dressed as a tiger, and Hoy running with a Team GB flag trailing him.
Other athletes involved in the PR-led video include boxing gold medallist Nicola Adams, high jumper Robert Grabarz and the Brownlee brothers.
Adidas UK marketing director Nick Craggs said: "Adidas is the Olympic brand and this video is a great demonstration of how we have supported Team GB and captured the mood of the nation.
"London 2012 will be remembered as the best Olympic Games ever and this is a celebration of Adidas' 'Take The Stage' campaign and the amazing achievement Team GB athletes have accomplished."
The video was completed in the last few days of the Olympics, with some of the filming taking place on a terrace above the Westfield Centre's car park.
Adidas senior PR manager Steve Marks came up with the idea for the video, which was produced by the 10 Group. Hill & Knowlton handled the PR behind the campaign.
The video was directed by Phil Bloom and produced by Rollo Jackson. Follow @johnreynolds10