The 19-year-old impressed Cheltenham boss Bobby Gould during a trial spell at Whaddon Road and he has earned himself a one-year deal at the club.
"I'm delighted to have secured Craig Dobson for next season," Gould told the club's official website.
"We invited him down for a trial and I think the stalwart supporters who go to the reserve games enjoyed his performances.
"We have given him a one-year contract but he is a very talented individual and we hope he flourishes with us. Craig is definitely a player for the future."
