The 29-year-old Republic of Ireland international has joined the Royals on a two-and-a-half year contract, the Barclays Premier League club announced.
Kelly becomes Reading's third signing of the January transfer window following the arrivals of midfielders Daniel Carrico and Hope Akpan.
Reading say the move is still subject to final ratification of all paperwork from the football authorities but expect that to be a formality, although Kelly was not signed in time to be involved against West Brom on Saturday.
Royals boss Brian McDermott is thrilled to have captured the defender, who was a key player for the Cottagers last season, making 34 appearances, but has lost his starting berth to Sascha Riether this term.
McDermott said: "I'm delighted to have Stephen here. 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 very young in football terms and at a really good stage in his career.
"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."
Reading chairman Sir John Madejski said: "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 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."
Fulham confirmed Kelly had joined Reading for an undisclosed fee, adding: "The club would like to thank Stephen for his contribution and wishes him well for the future.