The news comes hot on the heels of Franck Ribery's decision to prolong his stay at the Allianz Arena for another year.
"We're delighted that we've extended for another year with these two players - they've earned it," commented Bayern sporting director Hasan Salihamidzic. "Arjen Robben and Rafinha have an important role to play in our plans for next season."
Robben, 32, has made 209 competitive appearances since joining Bayern from Real Madrid in summer 2009, producing 138 goals and 99 assists. The Dutchman is a seven-time Bundesliga winner and has also lifted four DFB Cups, the 2013 UEFA Champions League, UEFA Super Cup and FIFA Club World Cup.
He holds the all-time record for most league title wins by a Dutch player (11), moving ahead of Johan Cruyff on the back of Bayern's triumphant 2017/18 campaign.
"I'm already wishing the new season could start now," said Robben. "It really hurt to go out of the Champions League in the semi-finals and not being able to play in the second leg. That's why I want to give it everything to make sure next season goes well, and be an important part of the team again."
Watch: Arjen Robben's top 5 Bundesliga goals
Two years Robben's junior, Rafinha is entering his eighth season as a Bayern player.
The Brazil international - who also played for Schalke between 2005-2010 - joined the club from Genoa in summer 2011.
🙌🏻GLORIA A DEUS🙌🏻— Rafinha Official (@R13_official) May 15, 2018
Nach sieben erfolgreichen Jahren beim FC BAYERN MÜNCHEN, ist es mir eine Ehre meinen vertrag um ein jahr zu verlängern...
After seven victorious years, It is a big pleasure to sign one more year with @FCBayern. #MiaSanMia pic.twitter.com/9f8n1ukZC2
"I'm very happy," Rafinha told Bayern's official website. "It's a dream come true playing for this club. I've been here for seven years and now I've added another one. I really feel at home in Munich, at one of the best clubs in the world."