The Montenegro international, who scored 13 goals in 31 appearances last term, has been hot property this summer, with Manchester United, Chelsea and Arsenal reported suitors.
City had been linked with the 23-year-old during Roberto Mancini's reign but successor Manuel Pellegrini now appears set to benefit from the club's lengthy pursuit.
A statement published on Fiorentina's official Twitter account read: "An agreement has been reached with Manchester City Football Club for the permanent sale of the player Stevan Jovetic."
City have already strengthened their squad with midfielder Fernandinho from Shakhtar Donetsk and winger Jesus Navas from Sevilla, with the latter's former team-mate Alvaro Negredo expected to follow in the coming days.
Negredo's transfer is yet to be formalised by City following Sevilla's announcement the Spain international had agreed a move to the Etihad Stadium, but it is clear Pellegrini is working to fill the gaps left in his forward line by the exits of Carlos Tevez and Mario Balotelli.
Jovetic, who can operate as a lone striker as well in front of the midfield, made his Montenegro debut in 2007 and scored his 10th goal for the nation in a friendly against Latvia last August.
A statement published on Fiorentina's official website later confirmed the transfer still hinges on Jovetic signing a contract in Manchester.