The 24-year-old spent four years at the Etihad, winning two Premier League titles, an FA Cup, two League Cups and two Community Shields.
In total, he made 135 appearances for City across all competitions, scoring 39 goals and assisting 45.
“We wish Leroy all the best in this new chapter of his career,” said City manager Pep Guardiola.
“Leroy has been part of one of the most special periods in this club’s history and he leaves with the best wishes of everyone here at Manchester City.
Director of Football Txiki Begiristain added: “From arriving as a fledgling young talent four years ago, we are proud of the contribution Leroy has made since joining Manchester City. He leaves with many friends and fond memories of his time at the Etihad.”
Sane joined from Schalke in the summer of 2016, making his debut as a substitute in the 2-1 win over Manchester United at Old Trafford.
He ended his first year at the club with nine goals and eight assists in 37 matches. Sane was a key part of City’s Centurions campaign the following season, scoring 14 goals and registering 19 assists as the Manchester-based outfit won the Premier League title and League Cup in emphatic style.
And in 2018/19, he played 47 times as we won an unprecedented clean sweep of English honours, scoring 16 and assisting 18.
Sane will start preparing for the upcoming season in Munich next week.
Bayern CEO Karl-Heniz Rummeigge said that Sane is an outstanding player who has proven his qualities over the past few years, especially in the national team.
“We’re very happy to welcome Leroy Sané to FC Bayern. Our goal is to gather the best German players at FC Bayern and the signing of Leroy emphasises this goal.”
Sané stated: “Bayern is a great club with big goals – and these goals suit me as well. I’m looking forward to the new challenge and can’t wait to train with the team.
“I know Hansi flick from the U21 national team, we had a very good relationship there. I want to win as many trophies as possible with FC Bayern, and the Champions League is the top priority.”
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Edited by Tokelo Martin Mokhesi
By Manchester City