The new role will see Bullock work alongside the board to drive the club forward, including community engagement, stadium improvements and commercial activities.
Bullock is the current Assistant Manager at Whitby Town and a former professional footballer playing at Bradford City, Hartlepool United, Cardiff City and York City.
Chairman Eddie McNamee said: "It is vital that now have someone at the helm who is committed to running the football club professionally and deliver the board's plans to create an organisation that commercially viable and committed to the community.
"Bully is a football man through and through and a great lad to boot. He will work alongside Graeme Hinchliffe and the board to ensure the club's finances are improved and development plans put in place."
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