The 17-year-old playmaker, who has caught the eye for the Royals' Under-18 and Under-21 sides, has put pen to paper on a two-and-a-half year deal.
"It's a great feeling to have signed for my boyhood club," Kelly told the club's official website.
"Having seen the likes of Jake Taylor, Jordan Obita and Aaron Tshibola given their chance, it gives us great motivation to work hard."
Academy director Eamonn Dolan added: "It's really good news. He's got himself a new professional contract, which is deserved. We believe he's going to continue to do well, work hard and give evidence. I'm sure he will go on to sign bigger and better contracts in the future.
"I remember seeing him as a nine-year-old and thinking 'wow, what a player'."