McIntyre, who took over at Linnets in the summer of 2020, led Runcorn to a fourth placed finish in the NPL West Division, before losing the play-off final against Marine.
He will now take over at his home city club, following the departure of Steve Watson.
Linnets chairman, Peter Cartledge said : "Calum has built a great and genuine rapport with all at Runcorn Linnets and has been incredibly diligent, honest and professional in everything he has done.
"It has been an absolute pleasure to have worked with him and have him as our manager. We are sure he is destined for big things in his football career.
"He has performed his duties with integrity, a real passion and a sense of pride, while assembling and developing a squad of players with undoubted talent and spirit.
"Calum deserves every credit for achieving this in his first completed season in charge.
"We thank Calum for his major contribution and total commitment during his time as our manager.
"He has put his heart and soul into the role and we wish him every success as he moves on to familiar pastures new."