Villa had two initial bids rejected by Genk for Benteke and there appeared to be a stand-off between the two clubs for a period on Friday.
But a deal was finally struck for Benteke, who has been a major target in recent weeks for Villa manager Paul Lambert.
Lambert 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.
