The 23-year-old joined Villa on a five-year contract for an undisclosed fee, believed to be in the region of £12m, after successfully completing his medical at Bodymoor Heath.
Ayew joins fellow former Ligue 1 players Jordan Amavi and Idrissa Gueye at Villa Park and could find himself playing against brother Andre, who signed for Swansea over the summer.
The former Marseille striker will be a direct replacement for Christian Benteke after he moved to Liverpool for £32.5m.
“I’m really pleased to bring Jordan to the football club,” Villa boss Tim Sherwood told the club’s official website.
“He is a fantastic young player who is perfectly suited to the Premier League.”