The Northern Ireland under-21 international, who can play either on the right side of midfield or as a full-back, leaves after just over three and a half years’ service to the club.
Mitchell played a total of eight competitive first-team games for Gers, with his last appearance coming in the 2-1 League Cup defeat at Forfar in August.
For much of the time since then, the 21-year-old has been on loan at Annan Athletic but that deal had expired last month and he had returned to Murray Park on a full-time basis.
Given he has turned both for the Light Blues and Annan this term, the former Manchester City trainee can only play again for the Galabankies this term.
FIFA rules dictate that a player can not appear for any more than two clubs in a single season so a second stint with the Borders side remains his best option for now.
Mitchell was an integral part of the side which won the SFL Reserve League last season and as skipper he collected the trophy when it was secured against Queen’s Park at Ibrox.
Manager Ally McCoist said: “Andy went down to Annan, played a few games there then came back up to us again last month.
“He is at a stage of his career where he needs to be playing regular football in order to continue his development.
“We could see when he came back to us that he had benefitted from featuring every week competitively down there.
“Sadly we can’t offer him what he needs at Rangers and we thank him for his efforts and wish him every success in the future.”
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