Robben moved to the Allianz Arena in August 2009 after finding himself out of favour at Real Madrid following the arrivals of Cristiano Ronaldo and Kaka.
The Netherlands international has gone on to enjoy a near decade of trophy-laden dominance with Bayern, winning seven Bundesliga titles and four DFB-Pokals.
Robben's crowning glory in a Bayern shirt came when he scored an 89th-minute winner to down domestic rivals Borussia Dortmund 2-1 in the 2012-13 Champions League final, a year after they lost a penalty shoot-out against Chelsea on home turf in the 2012 showpiece.
But the 34-year-old has confirmed that this campaign will be his last with the Bavarian giants.
Speaking to Omnisport during an official fan club visit, Robben said: "It's my last year at Bayern.
"It has been 10 beautiful years. But it's time [to leave] now."
Robben - who has 98 goals in 198 Bundesliga appearances - has started just seven of Bayern's 13 league matches this season, in part due to a knee injury.
Speaking earlier on Sunday, Bayern president Uli Hoeness suggested that it would be the last season for Robben and fellow veteran winger Franck Ribery, whose contract also expires next June.
Bayern have underperformed in the top flight this season and find themselves nine points adrift of pacesetters Dortmund after 13 matches.
It remains to be seen what Robben's next move will be, although he has previously hinted that he will finish his career at home-town club Groningen in the Eredivisie.