The club said in a statement: "The player contacted the club with his wish to leave in order to play closer to home and better manage his personal life.
"Following discussions, it was felt the only option was to allow the player to leave for the benefit of the team and Nathan personally.
"We have granted Nathan this request and wish him well for the future at his new club. We would also like to thank Nathan for all his efforts whilst donning the Boro shirt."
Cartman, 32, joined the Flamingo Land Stadium side in June 2020, having previously featured for Farsley Celtic, Darlington and Harrogate Town.
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