Murray-Jones, 19, moves to Forest on a three-year contract.
Forest's Head of Academy Chris McGuane said: “We’re delighted George is joining the B Team and that he sees Nottingham Forest as his next progression as a player.
“We have been monitoring his development for a period of time and we are all looking forward to seeing how he develops under the excellent guidance of our Head of Academy Goalkeeping Adam Skinner and our PDP Goalkeeping Coach Dominic Colman.
“George joining the Club adds to a strong group of goalkeepers, and we’re pleased we continue to attract exciting young players to the Club.
“Everyone in the Club wishes George the very best as he embarks on an exciting journey with Nottingham Forest.”
Murray-Jones said: “I’m really happy to have signed and can’t wait to get started.
“After discussions with the Club, I’m convinced this is the best place for me to develop my game and now I just want to get to work and have a good season.”