The 29-year-old, who can play on the left side of defence or midfield, has put pen to paper on a two-year contract at Villa Park with a further year's option.
Richardson has won eight senior England caps, scoring two goals, with his last appearance for his country coming in 2006.
His brief time as a full international came while he was with Manchester United, the club for whom he made his professional debut in 2002.
Richardson's stint with the Red Devils also saw him spend half the 2004/05 season on loan at Villa's midlands rivals West Brom.
After 81 United appearances over five seasons - in which he scored 11 goals for them - he went on to have a five-year spell with Sunderland between 2007 and 2012, playing 149 games and netting 15 times.
He has been with Fulham for the last two campaigns and leaves with a record of 48 appearances and six goals.
Villa boss Paul Lambert said on avfc.co.uk: "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 said: "Villa Park 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."
In coming to Villa, Richardson is being reunited with the club's new assistant boss Roy Keane, who was the manager who brought him to Sunderland and was also his team-mate at United.
Richardson said: "Roy is top-drawer, 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."
He added: "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."
Villa have also added defender Philippe Senderos and midfielder Joe Cole to their playing squad this summer.
Source : PA
Source: PA