City tweeted a picture of the 20-year-old Sane signing a contract, which is reportedly worth £37m (43m euros), plus add-ons, after he completed the medical examination in Manchester on Monday.
It’s time to #WelcomeLeroy to City! MORE ➡️ https://t.co/6njzfmEfqR https://t.co/fRn0Nk6pLY
— Manchester City (@ManCity) August 2, 2016
"One of the reasons I decided to join City was Pep Guardiola; he convinced me to come here and that I can continue to progress," said Sane on the Man City website.
Manchester City waiting for Sane to undergo medical check
"I know I will learn a lot under him and now I can take the next step in my career."
If the figure is confirmed, it will make Sane the most expensive German signing of all time.
"We have given the green light for the transfer. Those in charge of Manchester City behaved professionally at all times. There were difficult, but fair discussions," said Schalke's director of sport Christian Heidel.
Sane is a rising star in the Germany squad and has already posed for pictures with City fans in Manchester.
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The reported transfer figure seems astronomical given that Sane has made just 47 Bundesliga appearances, scoring 11 goals and creating seven more, since his debut in Germany's top flight in April 2014.
The fleet-footed forward made the last of his four international appearances for the world champions as a late replacement in last month's 2-0 defeat to hosts France in the Euro 2016 semi-finals.
Sane, who scored eight goals in 33 Bundesliga games last season, was missing when Schalke flew to their pre-season training camp in Austria on Monday.
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