"We're delighted we've reached agreement on a contract extension with one of the world's best players," Bayern chairman Karl-Heinz Rummenigge told the Bundesliga club's website.
"That is a sign of the big goals the team has set for the coming years."
Bayern said the new deal was signed with the 27-year-old before they lost 2-0 in the Champions League final to Inter Milan on Saturday.
"I made five more years," the Frenchman told a 25,000-strong crowd at Munich's central Marienplatz square, speaking in broken German, as the team were welcomed home.
He was referring to the five years he is contracted to play for Bayern, including the one year left on his old contract.
German media reported his annual salary would be around 10 million euros.
The France international, who joined Bayern in 2007 on a four-year deal, missed the match due to suspension after being sent off in the first leg of the semi-final against French side Olympique Lyon.
"My family and I are delighted that we're staying in Munich. The club has become a big family for me," Ribery said in a statement. "I am very happy that I opted to continue working together with Bayern."
Real Madrid, Barcelona and Manchester United had reportedly shown interest in the player, who is expected to have a big role for France at the June 11-July 11 World Cup in South Africa.
Ribery, who almost signed for Real last year, had said in the past months he would like to play in Spain or England to challenge for the top European title.
Ribery decided to stay at Bayern following an extremely successful season under new coach Louis van Gaal, winning their domestic league and Cup double and unexpectedly reaching the Champions League final.
"We will do everything to be back in the final in the coming years," Rummenigge said after a convoy of cars carried the team into the city centre.
