Bayern Munich agreed a £44.5million deal for Leroy Sane, with add-ons expected to take the fee closer to £55m.
City also inserted a 10 percent sell-on clause as part of the deal.Sane was expected to join Bayern last summer, but an untimely injury put the brakes on a move to the Bundesliga.
Pep Guardiola had hoped he could persuade Sane to sign a new deal at the Etihad Stadium, but the Germany winger rejected all attempts from City to tie down his long-term future.
Guardiola was always planning to regenerate his squad this summer after relinquishing the Premier League crown to Liverpool, but Sane's exit will intensify the search for new talent.
A centre back is considered the priority, with a left-back also on Guardiola's wishlist.
— FC Bayern English (@FCBayernEN)
Sane has signed a five-year contract with the Bundesliga champions, and signalled that winning the Champions League is the 'top priority'.
Leroy Sane told the club's website: “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. 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.”
Bayern CEO Karl-Heinz Rummenigge added: “We’re very happy to welcome Leroy Sané 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 Salihamidzic on successfully concluding the transfer.”