The 23-year-old, who joins from Lorient in France’s Ligue 1, helped his country to second place in the 2015 Africa Cup of Nations.
Villa were in the market for a striker after selling Belgian Christian Benteke to Liverpool for £32.5m.
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, moved to Swansea City after leaving Marseille in June.