Richardson, who can play at left-back or in midfield and counts Manchester United among his former clubs, joins Villa on a two-year deal following Fulham's relegation to the Championship.
The 29-year-old joins fellow new arrivals Philippe Senderos and Joe Cole in Paul Lambert's squad for the new Premier League season.
Lambert said: "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.
"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."
Richardson almost joined Villa as a schoolboy before opting for West Ham, and he said of the club's training ground: "The place has changed a lot, it's really magnificent and I'm delighted to be here.
"Villa Park itself has always been my favourite stadium out of all of the stadiums in which I've played in the Premier League. 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."
The move reunites Richardson with his former United team-mate Roy Keane - newly installed as Lambert's right-hand man.
"Roy is top-drawer," he told the official Villa website. "Outstanding as a player and excellent at man-management. He tells you how it is which is good for players and I'm delighted to be working with him again.
"I'm looking forward to working with the manager, too. He wants to play attacking football, he wants the team going forward and that's great. I haven't worked with him before, so I'm excited to start working with him now.
"For myself, I'm happy wherever I'm playing on the pitch, whether that's left back, left wing or centre midfield, even behind the striker.
"I'm happy to play wherever I'm needed. I've played in most positions - sometimes that can be a curse, sometimes that can be a good thing, but hopefully I can nail down a position here at the club."