City boss Pep Guardiola said: “He is a special talent, and an exciting player that I think our supporters will enjoy watching.
“He has great technical ability, is comfortable on the ball and there is much to admire about the way he plays football.
“He is fast, enjoys creating chances for others, works hard for the team and scores goals, too. He also has a very positive attitude and will fit in well with our squad.
“At 20, he is still developing as a player but he is already a member of the German national side and I think he will be a fantastic asset to our club. We are very happy he decided to join us.”