"I have always said I feel very good here. From a sporting perspective it is also the right decision," Robben said in a statement on Thursday.
"We have an outstanding team and we can have a lot of success in the coming years."
Only hours earlier Dutch international Robben refused to say whether he would extend his contract when asked by a small group of reporters at Bayern's training centre.
Robben, who joined from Real Madrid in 2009 and also played for Chelsea between 2004-7, won the German league and cup double in 2010 and helped Bayern reach the Champions League final in the same year when they lost to Inter Milan.
Injuries and a loss of form in the early part of this season cast doubt on his future at the club especially when he was criticised by former Bayern great Franz Beckenbauer, now the club's honorary president.
Robben underwent a groin operation in October but has since returned to his best form, helping Bayern reach the Champions League final against Chelsea on May 19 and the German Cup final against Borussia Dortmund seven days earlier.
A furious dressing room clash with fellow winger Franck Ribery late last month fanned speculation that their successful partnership in the Bayern front line, nicknamed "Robbery", could come to an end with the Dutchman reportedly unhappy with the way the club handled the incident.
"We are very happy to have extended Arjen's contract early for another two years," said club CEO Karl-Heinz Rummenigge. "Arjen is an extremely important player for Bayern and a guarantee for the club's successful future."
