The 24-year-old defender, who played 14 games for the Cottagers during a loan spell last season, has joined on a three-year deal for an undisclosed fee.
Richards is reunited with Fulham boss Kit Symons having worked together at international level, and the full-back admits he is looking forward to working with his compatriot again.
He said: “When I was on loan here last season, I settled in straight away with the lads and the staff, and I enjoyed the style of football that Kit Symons was trying to get the team playing. That made me want to come back.
“Kit’s a good manager, a good coach, and what he’s trying to get us to do will take the club forward, and we’ve got the players to do so. And we’ve already made some good signings this summer.
“In some of the games last season, we were unfortunate with the results, but with the crowd behind us this year supporting the lads, I think we can go on and do big things.”
Richards has also been on loan to Crystal Palace and Huddersfield Town since he began his career at the Swans in 2009.
He has five international caps for Wales having made his debut against Mexico in May 2012 and follows Andy Lonergan, Ben Pringle and Tom Cairney in making a move to Craven Cottage this summer.