The 35-year-old's previous deal was due to expire this summer, but he has now come to terms over a new contract which will see him remain at the Allianz Arena for a further 12 months.
Ribery joined Bayern in 2007 and has since gone on to make 385 appearances for the club across all competitions, scoring 117 goals.
"We are very pleased that Franck will be retained," sports director Hasan Salihamidzic told the club's official website.
"This season Franck has proved once again in the Bundesliga as well as in the Champions League and the DFB Cup outstanding achievements he is capable of and what a great quality he has. He is also one of our crowd pleasers."
Ribery added: "I am very happy to have another year for this big club to play. Munich has long been home to my family and me, so I'm very proud to be wearing the Bayern jersey in the new season."
The player has helped Bayern to 21 trophies during his 11 years at the club, including eight Bundesliga titles and the 2013 Champions League.