The 35-year-old's previous deal had been due to expire at the end of the season but it had been widely expected that an extension would be agreed.
After signing his new contract, he commented: "I'm very happy that I'll get to play for this great club for another year". "Munich has become a home for me and my family and I am very proud that I'll be wearing the (Bayern) shirt in the coming season".
It was Ribery's final pass which Arjen Robben converted for the winning goal at Wembley when Bayern beat Borussia Dortmund 2-1 in that year's Champions League final.
Ribery has helped Bayern to 21 trophies during his 11 years at the club, including eight Bundesliga titles and the 2013 Champions League.
Childish Gambino Debuts 'This Is America' On 'Saturday Night Live'
You can check out the full " This Is America " track on Apple Music/iTunes , as well as the song's official music video below. There's no release date yet for the new album, but we can probably expect it sometime before the end of the year.
Bayern, who are 16 points clear at the top of the table, play their final game of the season on Saturday, 12 May when they host Stuttgart.
"We are very pleased that Franck has been retained", said Bayern's sports director Hasan Salihamidzic.
"This season, Franck has once again proved in the Bundesliga as well as in Champions League and the DFB-Pokal the outstanding achievements he is capable of and what a great quality he has".
"As well as that, he's one of our fan favourites".