Allen, 16, is among eight teenagers to pen scholarship deals and join the club’s under-18s squad.
Chris Pooley, Harry Wood, Jake Oram, Justin Bennett, Max Adamson, Will Flint and Will Green will make the step up from Rovers’ under-16s.
Rovers, whose academy is Category Three, said on their official website they beat Category Two sides to capture the signing of Allen.
Cambridgeshire-born Allen signed for Norwich as a 13-year-old after a successful trial which included playing for the Canaries in an U13 Premier League Tournament against the likes of Manchester City, Chelsea and PSV Eindhoven.
Gary McSheffrey told Rovers’ official website: “They have all stepped up this year and grasped the opportunity. They are at a club where you will get opportunities because we are constantly evolving.
“I congratulate all of the players on their deals and look forward to watching them develop over the new two years.”