The 25-year-old, who has 24 international caps, has penned a four-year deal with the Villans.
Gueye played 176 games in Ligue 1 over the past five seasons.
"I'm really pleased to have brought Idrissa on board," Villa manager Tim Sherwood told the club's official website.
"He's been one of the best young midfielders in France for the last few seasons and there were a lot of teams trying to sign him this summer.
"I believe we are signing a player who is hungry to succeed, is entering what should be his best years and is perfectly suited to the Premier League."