Sane has penned a five-year contract with the Bavarians, and will wear the No. 10 shirt next season. He'll "start preparing for the upcoming season in Munich next week," Bayern said.
"We're very happy to welcome Leroy Sane to FC Bayern. He is an outstanding player who has proven his qualities over the past few years, especially in the national team," Bayern CEO Karl-Heinz Rummenigge said. "Our goal is to gather the best German players at FC Bayern and the signing of Leroy emphasizes this goal."
The move concludes Bayern's lengthy pursuit of the winger; the 24-year-old appeared to be on the cusp of joining the club last year.
It was reported last August that Bayern and City had agreed to a deal for Sane in the region of City's €100-million valuation, but the German international tore his anterior cruciate ligament in the Community Shield. The injury sidelined Sane for seven months, and talks between the two clubs dissolved in the interim with his current terms at the Etihad Stadium set to lapse in 2021.
Sane's only appearance this season was an 11-minute substitute's bow against Burnley on June 22. He bagged 39 goals across 135 matches in all competitions in four years with City following an initial £37-million recruitment from Schalke.
"FC Bayern is a great club with big goals - and these goals suit me as well," Sane said. "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."