The midfielder has cost a fee of around £3million and has penned a four-and-a-half year deal.
Lansbury was Forest's captain but had not played since December having been out injured before ex-boss Philippe Montanier felt he was not in the right frame of mind to feature.
He told the club's official site: "I am delighted to be here at Aston Villa.
"As soon as I knew Aston Villa were interested, I wanted to come here.
"It's the size and reputation of the football club that attracted me. It's a big, big name in the English game and I can't wait to get started here now.