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Kevin Prince Boateng became a full member of the club on Tuesday.
The 24-year-old footballer represented the Milan team throughout the season, but some of the rights to him still belonged to the Genoa team. However, after long negotiations, they were transferred to Milan.
As part of the agreement, the Italian champions will also have all rights to Alberto Paloschi, Marco Amelia, Nnamdi Oduamadi, and Gianmarco Zigoni, while Genoa regained midfielder Sokratis Papastathopoulos.
Both clubs will still control part of the rights to only one player: young striker Giancomo Beretta.
The financial details of the deal have not been disclosed.