The defender revealed on Twitter that he had opted to part ways with the Reds in order to start a "new chapter" in his career.
Now, the club has confirmed on its official website that Kelly has put pen to paper on a contract after passing a medical on Wednesday.
Kelly said: "I'm over the moon. It was a lot of travelling to get down yesterday, but I'm glad to have signed and I'm looking forward to the weekend.
"I'd heard about a potential move at the start of the summer, but I just wanted to concentrate on playing again in pre-season. I played a lot of games, which is what I needed. I've been out, fit, but not playing competitively all of last season. Now is the time at that age where I need to get back to playing week in, week out."
Kelly will wear the number 34 shirt at Selhurst Park.