The fullback has penned a two-and-a-half year deal with the Royals but, with the move awaiting ratification, will be unable to make his debut in Saturday's clash with West Brom.
Kelly has made just two Premier League appearances so far this term for the Cottagers but his new manager, Brian McDermott, is confident he will make an impact.
“I’m delighted to have Stephen here,” he 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.
“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.”
The club's chairman, John Madejski, has also hailed the arrival of the defender - who will take the No. 27 shirt at the Berkshire club.
“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," he said.
"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.”