Ribery, 30, joined the Bundesliga champions in 2007, and his current deal will expire in summer 2015.
The winger played a key role in Bayern's historic treble-winning season, where they became the first German side to win the DFB-Pokal trophy as well as the national and European titles.
With Pep Guardiola replacing Jupp Heynkes as Bayern's manager this summer, Ribery has committed his future to the club and wants to end his career in the Allianz Arena.
"We have discussed it all," said Ribery. "And saying 'yes' means 'yes' to me. We would not really need a player (to sign on).
"But I know we have to sign and this will happen as soon as possible, although there is no use to feel being in a rush.
"I am excited about being at Bayern Munich. I am very happy to, like I have never been in my life before. Why should I join another club? To move elsewhere and potentially feel less happy?
"If I am going to retire from the game as a Bayern Munich player I would like to do it as a 'Grand Seigneur', with a testimonial match."