A popular figure during his year at Whaddon Road, the 27-year-old hopes the club can bounce straight back to the Football League next season.
"I'd like to say a massive thanks to all the fans at Cheltenham because they have been unbelievable for me," Carson said.
"I'd like to wish everyone at the club good luck for the future and also thank Cheltenham for not standing in my way of moving.
"I made it quite clear I wanted to come back to the North East so I appreciate it.
"I'll definitely be looking out for the results and hope the club can bounce straight back to League Two at the first attempt."