The Republic of Ireland full-back has signed a two-and-a-half-year deal with the Royals for an undisclosed fee after falling down the pecking order at Craven Cottage.
"I'm delighted to have Stephen here," Reading manager Brian McDermott told the club's official 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.
"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."