The 21-year-old Benteke has put pen to paper on a four-year contract after agreeing personal terms and passing a medical.
Villa had two initial bids rejected for Benteke but finally agreed a fee before the player flew into Birmingham on Friday afternoon.
Benteke is Villa's eighth signing of the summer and takes their spending during that period to just under £25million.
He has been a major target in recent weeks for Villa manager Paul Lambert, who has watched the player in action on several occasions and feels he is the ideal kind of forward to supplement penalty-box predator Darren Bent and the speedy Gabriel Agbonlahor.
Benteke has netted three times in five games this season after being on target 18 times during the 2011-12 campaign in all competitions.
He was also scored for his country for the first time in the 4-2 win over Holland earlier this month in what was his fifth cap.
Benteke joins striker Jordan Bowery (Chesterfield) and midfielder Ashley Westwood (Crewe) in moving to Villa on transfer deadline day.
"I am still young and I have realised my dream. My dream was to come here and I am very happy," Benteke told Sky Sports News. "I hope I will be a success. I am motivated.
"It was difficult and I say thank you to Genk and everyone there. I will go forward for a new challenge.
"I think every player wants to come to the Premier League and I am very happy."
Bowery was the sixth new signing at Villa this summer following defenders Ron Vlaar, Joe Bennett and Matt Lowton, and midfield duo Brett Holman and Karim El Ahmadi.
His father Bert Bowery was also a striker who played for Nottingham Forest under Brian Clough before moving to the North American Soccer League in 1976.
Villa boss Paul Lambert said: "Jordan is a good player. The hunger will be there for him and he could surprise a few people. He's a good lad, he's strong and powerful. He's played over 100 games in the Football League and cup football, so he's battle-hardened.
"He's one for the future but if he steps up to the plate like I think he can then I would have no hesitation in throwing him in, none whatsoever."
Bowery, who played 40 games for Chesterfield in League One last season and also made eight appearances in Cups, scoring 12 goals in all competitions, said: "This is a Premier League club with so much history, a massive club, and I'm really excited."
The 22-year-old Westwood, meanwhile, has put pen to paper on a four-year deal which will keep him at Villa Park until the end of the 2015-16 campaign.
Westwood helped Crewe gain promotion to League One last season and is now relishing a crack at proving himself in the Barclays Premier League.
He said: "I see myself as a Michael Carrick-type of player, someone who stays out of the limelight and keeps it simple, retaining the ball and laying it off to team-mates.
"From the conversations I've had with the new manager (Paul Lambert) I think that will fit in perfectly here.
"He said to me that he's looking for younger lads to work with him, step up and lift this club to the next level and I'm really looking forward to the challenge. This is a fantastic football club, a massive club and I can't wait to get started really.
"It's a bit surreal right now but I'll get out training with the lads tomorrow morning and take it in my stride."