The 20-year-old made 15 starts and 15 substitute appearances for the Railwaymen, scoring three times.
He becomes Robins boss Gary Johnson's seventh new signing of the summer and will link up with his new team mates for the first day of pre-season training on Wednesday.
Cheltenham Town's summer signings:
Aaron Downes
Kyle Storer
Jack Munns
Amari Morgan-Smith
Harry Pell
Jack Barthram
Billy Waters