The 29-year-old Republic of Ireland international has fallen out of favour at Craven Cottage and has been allowed to join the Royals on a two-and-a-half year contract.
"I'm delighted to have Stephen here," Reading manager Brian McDermott told the club's website.
"He has played a lot of games in the Premier League and more than 30 times for his country. He's the kind of player I've been talking about - someone with great experience, but at 29 still young in football terms and at a really good stage in his career.
"I've always liked him as a player, and the first time I met him was at Kevin Doyle's wedding a while ago now and I thought he was a top guy. I know he's going to fit into the dressing room here really well.
"He's up for the fight, up for the battle, he's hungry, he wants to do well and I know he'll be successful for us."
Chairman Sir John Madejski added: "It's a great signing for Reading Football Club. He's a proven international and Premier League player and he seems like a lovely guy as well.
"We've had some great success stories with players from Ireland in recent years and I'm sure the signing of Stephen will be no different. I'm delighted he has signed and we all wish him very well during his career at Reading."
Kelly is Reading's third signing of the January transfer window - following midfielders Daniel Carrico and Hope Akpan to the Madejski Stadium.