No details of the deal for the 23-year-old have been confirmed but he joins new signings Adil Rami, Florian Thauvin, Valere Germain, Luiz Gustavo, Steve Mandanda and Clinton N'Jie at Stade Velodrome.
Amavi had been poised to sign for Sevilla last month, but they pulled out of the transfer after the defender's medical at the club.
France Under-21 international Amavi was expected to complete a move to the Liga side worth £8million before the deal fell apart, much to the ire of Villa owner Tony Xia.
"JA's medical report was good," Xia wrote on Twitter. "Someone hi-level [at Sevilla] didn't agree with the transfer&found a reason of injury history which is really unfair to JA.
"Very low. I have to say, from a businessman's viewpoint. Credibility and integrity is something very basic."