The 25-year-old arrives for an undisclosed fee, which British media estimated at nine million pounds ($13.94 million), having made 134 league appearances for the French side following his debut in 2010.
Gueye, who has 24 caps is likely to replace Villa's England midfielder and captain Fabian Delph who is expected to join Manchester City, according to local press reports.
"I'm really pleased to have brought Idrissa on board," Villa manager Tim Sherwood told the club website (www.avfc.co.uk).
"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 will join up with the beaten FA Cup finalists on receipt of his UK visa.
(Reporting by Tom Hayward; editing by Ken Ferris)
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