The 20-year-old defender became a fan favourite at Bower Fold during his time at the club, but will now move onto pastures new following his departure from the League One strugglers.
In total, he made 11 appearances for Celtic since joining in October.
He scored four goals, most notably netting a hat-trick in their 4-2 win over Liversedge at the beginning of January.
On his exit, Carson said: “I appreciate everyone at the club and what they have done for me.
“I loved every minute of it, so thank you for having me! I’ll be down when I can to cheer the lads on.”
Photo credit: Phill Smith Photography
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