Ayew's arrival follows Villa's summer acquisition of fellow Ligue 1 players Jordan Amavi and Idrissa Gueye.
The Midlanders, who also lost Fabian Delph to Manchester City, have signed Scott Sinclair, Micah Richards and Mark Bunn since the end of last season.
"I'm really pleased to bring Jordan to the football club," manager Tim Sherwood said.
"He is a fantastic young player who is perfectly suited to the Premier League."
His older brother, Andre Ayew, also moved to Swansea City after leaving Marseille in June.