"We are delighted to have kept two key players with us," said Bayern CEO Karl-Heinz Rummenigge in a statement. "Franck and Daniel were outstanding in the past season and we counted on them to make the difference in the crucial games."
Frenchman Ribery, 30, enjoyed his most successful season since joining in 2007, scoring 10 goals in the Bundesliga and setting up another 14.
"I had promised this to the fans and now the contract is done," crowd favourite Ribery said. "For me and my family Munich is our second home and I am sure there are still one or two titles out there for us to win in the coming years."
The deal will also be welcomed by Pep Guardiola, the former Barcelona coach who takes over at Bayern this month, with Bayern having also signed midfielder Mario Götze from rivals Borussia Dortmund for next season.
