Reports emerged earlier this morning that the 29-year-old was preparing to undergo a medical with the Midlands outfit today.
Richardson, who spent part of his youth career at Villa, also has an option to extend his contract by a further year.
"Villa Park itself has always been my favourite stadium out of all of the stadiums in which I've played in the Premier League," Richardson told the club's official website. "It's got great atmosphere, the fans are magnificent and I'm really looking forward to playing here. I know I'm going to love it."
Manager Paul Lambert added: "Kieran will complement many of the players here well with what he brings.
"He will add pace, a great deal of experience and he knows the Barclays Premier League. He's played a lot of games for a lad who has yet to turn 30."
Richardson will also play under the guidance of assistant boss Roy Keane.