The 24-year-old Germany international has signed a five-year contract with the Bavarians and will inherit Philippe Coutinho’s number ten jersey for the 2020/2021 season.
In four seasons with Manchester City, Sane won two Premier League titles, one FA Cup and two League Cups but he failed to win Europe’s premier club competition in England.
"FC Bayern is a great club with big goals and these goals suit me as well," Sane said after completing the deal.
"I'm looking forward to the new challenge and can't wait to train with the team.
"I know Hansi Flick from the under-21 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."
Sane also paid tribute to his former club, who acquired him from Schalke 04 in the summer of 2016.
“Thanks so much for the great time and all the support over the last 4 years,” he wrote on Twitter.
“It has been a really intense and successful time which I surely won’t forget.
“We won many games, scored a ton of goals, broke a couple of records and celebrated 7 trophies together.
“Thanks to all the fans, to the staff and to my team-mates! I will always remember this time with great joy and pride.
“Also thanks to my coach who has made me a better player and has a large share of my PFA Young Player of the Year award in 2018.
“I’ve learned a lot and I’m very proud to have been part of this journey.”
