The 24-year-old winger has agreed a four-year deal with the Premier League-bound club, following a successful loan spell last season.
El Ghazi scored six goals in 37 appearances after joining from Lille in August, including the opener in last month’s play-off final victory over Derby.
That clinched Villa’s return to the top flight after a three-year absence and boss Dean Smith believes El Ghazi, who came through the ranks at Ajax, has what it takes to thrive among English football’s elite.
“Anwar proved to everybody at Wembley how good a player he can be for Aston Villa,” said Smith.
“He’s ready for the step up to the Premier League and he’s a young player who has an awful lot of potential. It’s now my job and the job of the coaching staff and Anwar himself to fulfil the potential that he undoubtedly has.
“He’ll be a great addition to the squad for next season.”
Villa triggered a clause in the original loan deal with Lille in order to make the move permanent.
El Ghazi becomes the club’s second signing since winning promotion and the second winger, following the arrival of Jota from rivals Blues.
Villa are also expected to confirm the signing of Wolves defender Kortney Hause in due course.
The 23-year-old, who also enjoyed a successful loan spell with Villa last season, will join in a £3million deal.