The 19-year-old former Shakhtar Donetsk player, who featured in all three of Ukraine's matches at Euro 2016, arrives from Russian club FC Ufa.
Zinchenko's arrival at the Etihad Stadium follows those of Ilkay Gundogan and Nolito this summer.
A tweet from the club read: "Manchester City are pleased to announce the transfer of Ukrainian midfielder Oleksandr Zinchenko from FC Ufa."
Source: PA