The 35-year-old joined Bayern as a boy in 2000 and has played a club record 743 games for them, winning 33 trophies, including 12 Bundesliga titles, six German Cups and two Champions Leagues.
Muller said on Instagram on Saturday he respected the decision of the club although he wanted to stay on, but he didn't reveal plans for the future.
Bayern stated squad planning for the future as the reason for the decision to part ways with their fan favourite who made his first-team debut in 2008 but who's only played sporadically this season.
Bayern said he would get his own testimonial and that his last matches would be at the Club World Cup in summer in the United States.
His last home game in Munich will either be on May 10 in the Bundesliga against Borussia Monchengladbach, or, ideally, the May 31 Champions League final.
"Even after all these years, regardless of my playing minutes, I still have a lot of fun being on the pitch with the lads and fighting for titles together for our colours. I could have easily imagined myself in this role next year as well," Muller said on Instagram.
"But the club made a conscious decision not to negotiate a new contract with me for next season. Even if this was not in line with my personal wishes, it is important that the club follows its convictions.
"I respect this step, which the board and supervisory board certainly did not take lightly."
He added in a Bayern statement: "The special connection to the club and our fantastic fans will always remain. What I want as a farewell should be clear: titles we can celebrate together, and moments we'll remember fondly for a long time."
Bayern president Herbert Hainer said that Müller "is the definition of a Bavarian fairytale career; he grew up in Bavaria and with Bayern. From Ammersee to the Allianz Arena, as far as Asia and America.
"He ranks among the most outstanding personalities in FC Bayern history."
But there's no longer a place for Muller, celebrated for being a 'Raumdeuter' (interpreter of space) in the opposition half, which resulted in 247 goals and 273 assists for Bayern, plus 45 goals in 131 Germany caps highlighted by the 2014 World Cup title.
"Thomas doesn't play according to the textbook - he writes his own," board member for sport Max Eberl said.
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