Reynolds has been in charge at Irongate since December 2016 and led them to promotion to the EVO-STIK League Premier Division last season.
He will take charge of Brig for the final time this weekend at home to Basford United, before joining the National League North club.
Club chairman, Fran Doyle, said: “During the past two weeks there has been much speculation regarding the future of Neil Reynolds.
“The speculation arose following an approach by FC United of Manchester for Neil to become their manager.
“This approach was turned down by Bamber Bridge FC as Neil was under contract to this club.
“Discussions between Neil and both clubs continued and following the approval of a compensation agreement with FC United of Manchester, Bamber Bridge Football Club have reluctantly agreed to release Neil from his contract with the club.
“Neil has served Bamber Bridge Football Club as both a player and manager with great skill, dedication, integrity and passion for over two decades. Under Neil’s management the club has won the Integro cup and were promoted to the NPL Premier Division.
“On behalf of everyone at Bamber Bridge Football Club we offer our thanks to Neil for everything he has done for this club and wish him every success for the future.”
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