The 24-year-old has signed a five-year deal after the German champions agreed a deal thought to be worth €45 million plus add-ons.
“FC 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,” Sane told Bayern’s website.
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.
The German international made 135 appearances for City since a 2016 switch from Schalke, scoring 39 goals and winning two Premier Leagues, an FA Cup, the League Cup twice and two Community Shields.
FC Bayern CEO Karl-Heinz Rummenigge called Sane an outstanding player who fulfilled Bayern's goal of signing the best German players on the market.
We’re very happy to welcome Leroy Sans to FC Bayern. He is an outstanding player who has proven his qualities over the past few years, especially in the national team. Our goal is to gather the best German players at FC Bayern and the signing of Leroy emphasises this goal. I would like to congratulate Hasan Salihamidžić on successfully concluding the transfer.
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The former Schalke man made his debut for Die Mannschaft in 2015, and has represented his country 21 times, scoring five goals.