The 34-year-old joined the Bavarians in 2009 and instantly formed a formidable attacking partnership with Frenchman Franck Ribery, who is also likely to leave at the end of the season.
"I can say that this is my last year (at Bayern) and it is good like that," Robben told reporters after a meeting with fan groups. "I have taken the decision, personally, that this will be my last year.
"I think it is the right moment after 10 years. The club moves on and I may move on. It is the end of a very good and long period."
Robben has scored 98 goals in 198 Bundesliga games for Bayern and, since his arrival in 2009, he has played in three Champions League finals -- in 2010, 2012 and 2013 -- winning the title at the third attempt with Bayern.
He has also won seven German league titles, including the last six in a row, and four German Cups with the Bavarians.
Robben, who has also won league titles with PSV Eindhoven, Chelsea and Real Madrid and featured in the 2010 World Cup final for the Netherlands, added that he had no plans to retire.
"I may move on. I won't stop completely yet," he said.
(Reporting by Karolos Grohmann; Editing by Ian Chadband)
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