The 22-year-old has joined for an undisclosed fee reported in British media to be around seven million pounds ($10.9 million).
"I'm really pleased Jordan decided to choose Aston Villa over the other options he had and opt to continue his development with us," manager Tim Sherwood told the club's website.
"He is only 22-years-old but he is vastly experienced for someone that age. He has played over 140 games in Ligue 1 and is a really exciting young player.
"I know he is very highly rated over in France so we are delighted to get this deal over the line."
Veretout is the fourth player to arrive at Villa Park from Ligue 1 during the close season following the signings of Jordan Amavi, Idrissa Gueye and Jordan Ayew.
(Reporting by Michael Hann, editing by Ed Osmond)
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