The Cottagers have not disclosed the transfer fee they have had to pay the Black Cats for the services of the 27-year-old, who is overjoyed with the move.
"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," said Richardson.
Fulham manager Martin Jol too is pleased with the arrival of the former Manchester United player.
"Kieran is a proven top-level player, who has the versatility to play a number of positions," he said.
"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 joined Sunderland from United in 2007.