The 19-year-old has been with the club since the foundation phase and has shown consistent improvements from season to season and in recent campaigns he has both trained with the first-team squad and been involved in the first-team set-up on matchdays.
Shelvey was on the substitutes' bench for Forest's Emirates FA Cup tie at Chelsea last season before he made a short-term loan move to Truro City and made a number of appearances for the Southern League Premier Division South side before returning to The City Ground.
The young shot-stopper is thrilled to put pen to paper on a new deal and said: "I'm delighted to sign this new deal with the club. I have been here from such a young age and to get this contract done fills me and my family with a lot of joy.
"I'm excited to see what the future holds for me at the club that I love!"
Under 23s' head coach Andy Reid said: "We are pleased to get George's deal over the line. He's a goalkeeper with a lot of ability and potential and with lots of hard work and dedication to come from George, we believe we have a goalkeeper who can play at the top level."