Villa announced last Tuesday they were in negotiations with the Danish outfit over Helenius, adding that they expected to secure his transfer - subject to a medical and personal terms - within 10 days.
It has now been confirmed that the 22-year-old has put pen-to-paper on a three-year deal with the Midlands club.
Denmark international Helenius told the club's official website: "This is a big opportunity for me, a big dream to play in the Premier League with a club with the history of Aston Villa, and I'm very excited."
Helenius, who has two senior international caps, came through the youth ranks at Aalborg and the 6ft 5in frontman was the second-highest scorer in the Danish league last season with 16 goals.
"I learnt a lot over the past few seasons with (Aalborg coach and former Villa defender) Kent Nielsen as my manager," he added.
"He was a player here at Villa and, while I have always been a good finisher, he taught me to be more aggressive and determined when I don't have the ball.
"He showed me how to work hard and this will help me in this league."
Helenius becomes Villa boss Paul Lambert's fourth summer recruit following on from Jores Okore, Leandro Bacuna and Aleksandar Tonev.