"The deal will be finalised next week after a medical," Genoa president Enrico Preziosi told the club website.
"Frey was highly motivated to join the club, agreeing to reduce his wages, in order to re-start his career with Genoa," Preziosi said.
The 31-year-old spent the five previous seasons at Fiorentina. Since arriving at Inter Milan as a teenager, he has also played for Verona and Parma.
Frey made two appearances for France and was included in the Euro 2008 squad but quit international football the same year after being overlooked by the then coach Raymond Domenech.
Genoa finished 10th in Serie A last season.
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