The 26-year-old, who has scored 10 Premier League goals this season, has signed a five-and-a-half-year deal at the Etihad and will be a major addition to their attacking arsenal.
Liam Rosenior said his challenge is to take Chelsea to the "next level" as he prepares to take charge of the Blues for the first time in Saturday's FA Cup trip to Charlton.
Manchester City added to their attacking arsenal on Friday with the signing of Antoine Semenyo from Bournemouth for a reported £65 million ($87 million).