The ex-Real Madrid and Chelsea flier, 34, told Omnisport: "It's my last year at Bayern.
"It has been 10 beautiful years. But it's time [to leave] now."
Robben hit 37 goals in 96 games for Holland and famously notched Bayern's 89th minute Champions League final winner against Borussia Dortmund at Wembley in 2013.
So far he has 98 goals from 198 games for the Bundesliga giants.
Robben exited Real for the Allianz Arena in August 2009 after Cristiano Ronaldo and Kaka switched to Madrid.
Bayern president Uli Hoeness had hinted at Robben's announcement earlier on Sunday.
Hoeness suggested the former PSV Eindhoven favourite and French winger Franck Riberry, 35, would move on in the summer when their contract ends.
It underlines a period of dramatic change for the current German champions, who after 13 matches are nine points behind leaders Dortmund.
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