Grabbing the stadium microphone minutes after their 3-0 Bundesliga win over St Pauli on Saturday, the German international told the fans: "I have extended my contract and will stay here until 2016. Long live Bayern.
"I think we have a great group here and my heart is red and I prefer to win the Champions League with Bayern than with Real Madrid," he later told reporters after his team climbed to fifth position.
According to media reports, Inter Milan, Manchester United and Chelsea were also interested in signing the 26-year-old.
Schweinsteiger has become an influential figure for club and country and helped Germany to a third-place finish at the World Cup in South Africa earlier this year.
Bayern coach Louis van Gaal recently urged the club to consider selling Schweinsteiger at the end of the season should he refuse to sign an extension, so as not to lose out on a transfer fee worth tens of millions of euros.
The player, who has been at Bayern since the age of 14 and has won five German championships and five German Cups, hinted earlier this season that he could leave.
Bayern have already extended contracts to 2014 or beyond with several other leading players including Franck Ribery, Philipp Lahm, Thomas Muller and Holger Badstuber.
In the past 18 months Schweinsteiger has shed his previous image as a hugely talented yet inconsistent player.
CHAMPIONS LEAGUE
He and Dutch striker Arjen Robben featured prominently in last season's domestic double and Bayern's run to the Champions League final where they lost to Inter.
Schweinsteiger is able to change the pace and rhythm of the game with a simple turn of his body, a slicing pass or a fierce long-range drive.
'Schweini', as he is affectionately known, made sure the injured Michael Ballack was hardly missed by Germany at the World Cup.
A versatile player, who can shine as a holding or attacking midfielder, has blossomed under Van Gaal who employs him in his favourite position in the centre instead of the wings.
Adored by fans and club bosses alike it was no accident Bayern chief executive Karl-Heinz Rummenigge addressed Schweinsteiger at last month's annual general meeting in front of 2,000 people.
Rummenigge told the midfielder the Bavarian club wanted him to stay and would do everything to keep him.
"It is a very good thing for the club that such an important player has made such a commitment to the club," a beaming Bayern president Uli Hoeness said on Saturday.
Schweinsteiger had for months refused to commit to Bayern, saying the prospect of playing abroad was attractive.
His new deal will make him richer and his club, who are through to the Champions League knockout stages, more powerful in the coming seasons.
