Wilson has yet to play for City this season and said that the move will allow him to get more first-team football under his belt.
"I'm looking forward to my time at Cheltenham," said Wilson in a club statement. "I needed to come out and play first-team football. It's not working out for me at Bristol City right now so I just want the chance to play again.
"Cheltenham Town is a good club and they have been close [to promotion] in the last few seasons so it is a good place to be."
Wilson has played 34 times for the City first team.