The France international, who has been at the club since 2007, had agreed to a four-year contact extension with the Bavarians at the start of the month and has now signed on the dotted line.
"I'm very happy," Ribery told the club's official website. "I've always said that I feel at home at Bayern.
"I have a good feeling here, for both myself and my family, and I hope things continues like last year!"
The 30-year-old winger was one of the key performers in Bayern's historic treble success and has already been asked by new boss Pep Guardiola if he would like to occupy a more central attacking role next season.