The attacker will spend the 2014-15 campaign on loan at the Stadio Luigi Ferraris after failing to make an impact at San Siro.
The Luigi Ferraris outfit was in the market for a new striker following the departure of Alberto Gilardino to Guangzhou Evergrande and the club sees the 29-year-old Matri as the perfect replacement.
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Matri joined Milan from Juventus in the summer of 2013, but failed to make an impact with the San Siro side and was shipped out on loan to Fiorentina for the second half of last season.
He returned earlier this summer, but has now left the club on another temporary deal after he was told he does not play a part in head coach Filippo Inzaghi's plans for the future.
Matri started his professional career with Milan and also wore the jerseys of Prato, Lumezzane, Rimini and Cagliari before joining Juventus in January 2011.
The attacker will now be looking to relaunch his career at Genoa after a disappointing spell with Milan.