The 27-year old Dutch defender has signed a three-year deal with the West Midlands club even after it appeared that the deal had fallen over.
Vlaar was in lengthy negotiations with Villa regarding the contract with some reports earlier this week saying that a deal had not been reached but now it has been sorted pending a medical.
"It's a strange feeling to leave Feyenoord, but it's a dream come true to play in the Premier League," he told the Dutch clubs official website.
"We (the club and myself) spoke again today and sorted some things out. It was a lively conversation and Aston Villa apologised for the way they acted in the last weeks."
He added: "I can imagine that the Feyenoord fans, at this moment, aren't happy with me, but I hope they understand why I'm leaving."