The 25-year-old has penned a four-year deal at Villa Park and will join up with his new team-mates upon receipt of his UK visa.
Gueye has made 24 international appearances and played 176 games for Ligue 1 side Lille over the past five seasons.
Villa manager Tim Sherwood told the Aston Villa???s website: “I’m really pleased to have brought Idrissa on board.
“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.”
Gueye is Tim Sherwood’s third summer signing, following the arrivals of Micah Richards and Scott Sinclair from Manchester City.
Meanwhile, Aston Villa skipper Fabian Delph is expected to undergo a medical at Manchester City this weekend ahead of completing a move to the Etihad Stadium.??