Richardson has spent the past two campaigns with Fulham, making 48 appearances and scoring six goals.
His efforts were not enough to prevent relegation last term, and he is the latest player to leave Craven Cottage.
The likes of Brede Hangeland, Damien Duff and Steve Sidwell have all moved on from the London club following their drop into the Championship.
Richardson joins Philippe Senderos and Joe Cole in moving to Villa Park as Paul Lambert looks to improve on last season's 15th-place finish in the top flight.
He has over 200 appearances worth of Premier League experience with Manchester United, West Brom and Sunderland.
"Kieran will complement many of the players here well with what he brings," said Lambert.
"He will add pace, a great deal of experience and he knows the Premier League. He's played a lot of games for a lad who has yet to turn 30.
"The grounding he gained at Manchester United has stood him in good stead and he knows what it is to compete in this league and to win things and that's important. I'm delighted he's joined us and we're really looking forward to working with him."
