Button finished fifth to become his country's 10th world champion, with closest rival and team mate Rubens Barrichello suffering a late puncture and crossing the line eighth after starting his home race on pole position.
Red Bull's Sebastian Vettel, the 22-year-old German who had needed to finish in the top two to have a chance of staying in the reckoning, took fourth place.
Brawn, who had needed only a point to be sure of the championship, become the first team to take the constructors' crown in their first full season.
Poland's Robert Kubica was second for BMW-Sauber with McLaren's outgoing world champion Lewis Hamilton taking third place after starting 17th.
Congratulations to Jenson on a fabulous season...