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 this weekend.
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."
Kelly, who can play on either the right or left of defence, came up through the youth ranks at Tottenham before breaking into the first team at White Hart Lane.
After several spells out on loan, he joined Birmingham permanently in 2006 and spent three years at St Andrew's - incorporating a loan stint at Stoke - before making the move to Fulham, who helped reach the Europa League final in the 2009/10 season.
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."