Charlton, 20, was most recently with Blyth Spartans, following a spell at South Shields.
He was also a part of Middlesbrough's youth step up in 2019.
He said: "I'm delighted to have it all done now. Now it's all confirmed, I can concentrate on getting into the best possible shape for pre-season."
Manager Danny Grainger added: "Kieran's a player who suits everything we do.
"He's got high standards, is a good organiser and good communicator.
"He's also a winner and driven to be successful. I can't wait to see him in a Reds shirt and I'm sure supporters will feel the same."