Rovers' Memorial Ground is being redeveloped, and the team will spend the next two seasons playing in Gloucestershire. The club also had offers to relocate to Yeovil or Swindon.
Rovers chairman Ron Craig said: "The decision to share with Cheltenham was made with fans in mind as it's the easiest option for travelling. The quality of the pitch was also a consideration.
"We'd like to thank Swindon Town and Yeovil Town for their co-operation during this time, and we look forward to working closely with Cheltenham in the coming months.
"We're also looking forward to the continued support of our loyal fans during this difficult time away from the Memorial Stadium.
"We really appreciate all the backing they've already given us, and hope that they continue to do so while we play away from Bristol."
Rovers will definitely be in League One next season, while Cheltenham go into the final day of the season with their survival still not secure.