The 34-year-old made the announcement via Bayern Munich's website in an interview, saying "of course, one thinks a lot about the future. That was already the case last year when I extended for another year. Ten years has been an incredibly nice and long period.
"I'm 35 in the summer and I think it's good for everyone, including myself and the club. I'm still very happy at the club, but the point is also coming where you say, now it's okay."
Robben joined Bayern from Real Madrid in 2009 and has since made over 300 competitive appearances for the Bavarians, winning seven Bundesliga titles, four DFB Cups and famously netting the winner in the 2013 UEFA Champions League final against Borussia Dortmund.
Watch: Robben's top 5 goals
The club legend also confirmed that he has not made a decision on whether he will end his career.
"That's still open, anything can happen there," Robben said. "Therefore now was the best time to announce it. Everything is clear to our fans and to the club and everyone knows that it's over at the end of the season. I also have enough time to think about the future and what the next step will be. It may be that I'll stop altogether, but also that I carry on."
Bayern president Uli Hoeneß also commented on the Dutchman's departure while visiting a fan club in the Bavarian town of Kersbach, saying that Robben's long-time partner on the wing, Franck Ribery, 35, is also set to leave at the end of the season: "It is highly likely that they're both in their last year at Bayern."
Once the duo leave in summer 2019 it will mark the end of an era at the record Bundesliga champions, the pair having earned the nickname 'Robbery' over the years for their pincer-like attacks on opposition defences.
After almost 10 years at the club, @ArjenRobben has confirmed that this will be his last season at #FCBayern 😢— FC Bayern English (@FCBayernEN) December 3, 2018
We will cherish these remaining months with you, Mr. Wembley! ❤️#MiaSanMia pic.twitter.com/9zPhAxPEh3
Robben's early years at Bayern were often plagued by injury but he has arguably got fitter and better with age, becoming more effective from his customary position as an inverted winger on the right flank. His signature move of cutting inside onto his favoured left boot before rifling a shot into the net has gone down in Bundesliga folklore - not that it has become any easier to stop.
His legacy is further bolstered by his record of 98 goals in 198 Bundesliga outings for Bayern, making him the club's second-highest non-German scorer of all time, behind only Robert Lewandowski (113).