"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.
Van Buyten, at 35, was given a one-year extension to his deal following another solid season despite being second choice behind Jerome Boateng.
The Belgium international, who joined the Bavarians in 2006, will also be an option next season following the cruciate ligament injury suffered by central defender Holger Badstuber who will be out for about 10 months.
Bayern, who set a record for fewest goals conceded in the Bundesliga with just 18 in 34 league games, became the first German club to win the treble after also adding the German Cup this month.
Wycombe Wanderers forward Richard Kone named as our League One player of the season: ‘Even as I was signing the contract to join the club, I was like “I’m going to wake up soon!”’
JULES BREACH: There won't be a dry eye in the house when Everton bid farewell to Goodison Park... but the future looks bright at their new state-of-the-art stadium
