The Japanese manufacturer agreed to the deal after a three month search for a new owner.
Honda announced in December last year that it would be pulling out of F1, blaming the global economic crisis.
The industry has been rife with speculation that Richard Branson's Virgin Group would buy the team but it has now been confirmed that it will now operate as Brawn GP, with engines supplied by McLaren Mercedes.
Honda, which spent more than £300m a year on F1, made the headlines last year when it scrapped sponsorship deals and instead covered the car in an image of the Earth to promote its own green credentials.
Brawn GP has yet to clarify its sponsorship position but is expected to make an announcement ahead of the opening race of the season -- the Australian Grand Prix in Melbourne on March 29.
The team has confirmed it will continue to employ British driver Jenson Button and Brazilian Rubens Barrichello, but has reportedly dropped Bruno Senna, nephew of the late champion Ayrton Senna.
Yesterday, the newly established Formula One Team Association announced that all F1 teams will introduce a 50% cut in operating budgets for the 2010 season, with further measures to reduce costs, boost revenue and improve the public image of the sport.