The 29-year-old has had something of a nomadic career thus far, playing for Hajduk Split, Blackburn Rovers and Dnipro Dnipropetrovsk before joining Fiorentina.
The signing of Kalinić gives Milan manager Vincenzo Montella another option to call upon in the attack, joining another summer signing in Portuguese global André Silva and 19-year old youth system product Patrick Cutrone.
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The seven-times European champions said they had signed Kalinic "on loan with an obligation to buy", but did not specify the length of the loan period. Kalinic signed a four-year contract through to June 30, 2021. He ended up successfully passing his medical with the Red and Blacks on Monday, and has now sealed the transfer for a fee rumoured to be in the range of €25 million.
He will compete with fellow new arrival Andre Silva for starting striker duties at Milan, with youngster Patrick Cutrone also still at the club.
Kalinic first moved to Italian football back in 2015, scoring 33 goals in 83 appearances since.
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Milan will now be hoping to challenge Juventus, Napoli and Roma for the Serie A title after a promising and active transfer window, with players like Leonardo Bonucci, Mateo Musacchio, Ricardo Rodriguez and Hakan Calhanoglu all being brought in.
Milan won 3-0 away to Crotone in their opening game of the season on Sunday.
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