The 24-year-old has been in fine form for the Bees so far this season, scoring 14 goals in just 25 appearances.
That form attracted the interest of West Ham United, but Villa emerged as favourites to sign the striker after the Hammers pulled out of a deal this week.
Steve Bruce's side have now secured the signature of the former Rochdale man for an undisclosed fee, thought to be worth as much as £15m including add-ons.
"I'm delighted to be at a club like Aston Villa. With its history and tradition I can't wait to start working hard and helping the team," he told the club's official website.
"It all happened quite quickly and now I'm looking forward to meeting my new teammates tomorrow and beginning a new chapter in my career."
Hogan could make his Villa debut against Nottingham Forest in the Championship on Saturday.