The 27-year-old, who was born in London, signed a three-year deal, with an additional year's option, for a undisclosed fee.
He told Fulham's official website: "I'm delighted that my transfer to Fulham has been completed and now I'm eager to start training for my new club straight away and pulling on the white shirt for the first time."
Richardson made 149 appearances for the Black Cats after signing from Manchester United in 2007 shortly after lifting the Premier League trophy.
Fulham manager Martin Jol said: "Kieran is a proven top-level player, who has the versatility to play a number of positions.
"He will bring all-round quality which will add strength to our squad and I'm confident that he will adapt well to our style of football, and make an impact for us."
Richardson's career began at West Ham, before he sealed a move to Old Trafford.
He made 81 appearances in almost five years with the Red Devils, which included a loan spell at West Brom.
Richardson joined Sunderland in July 2007 for an undisclosed fee following their return to the top flight.
Source: PA
Source: PA