The 21-year-old came through the academy at City before securing a temporary switch to Brunton Park in November.
Chantler has now signed an 18-month contract with the Cumbrians after impressing boss Greg Abbott.
Abbott told the club's official website: "Chris is one we think will develop into a really good footballer.
"He's been here for six weeks already with us and we like him a lot. He has terrific ability and can play a number of positions down that left-hand side and in the centre of the pitch."