Fiorentina allowed the Croatia international to leave their summer training camp twice earlier in July due to serious family issues, including a robbery.
Kalinic told Sky Italia last month that he knew that Serie A rivals AC Milan were interested in signing him and that he wanted to join the club.
Giovanni Simeone, another forward, joined Fiorentina on Wednesday from Genoa.
(Reporting by Silvia Recchimuzzi in Gdynia; Editing by Christian Radnedge)
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