Furman, 32, returned to the United Kingdom after five seasons in South Africa with SuperSport United where he became club captain and national team captain at one stage - whilst winning three trophies in the PSL.
His move back to England was motivated by wanting to be near his parents after the birth of his new child which all happened during the global coronavirus pandemic.
But his one-year deal with the League Two club has now expired and the two parties have agreed to mutually part ways after he made just nine starts as they finished 10th in the 24-team division.
"Dean is a great lad and probably up there with one of the best professionals I've worked with," head coach Chris Beech told the club's website.
"You'd expect that from someone of his stature. He's captained his national team and played on that international stage, and fortunately for us those traits have influenced some of [the] younger players throughout this season, and that's been a big plus.
"By his own admission, Dean hasn't played as much football as he'd have liked this season. Those opportunities have been limited in the main by the tremendous run we went on in the first half of the season, and the form that Callum [Guy] showed playing in the slot that we brought Dean in to fill.
"He goes with my best wishes and I've no doubts that whatever he chooses to do next will be a success because he has that attitude and professionalism about him."
The defensive midfielder featured in 20 games across all competitions and registering two assists in his solitary campaign for the Cumbrians.