Meanwhile, Gale was suspended from duty last month pending an investigation into a historic offensive tweet sent in 2011.
Moxon and Gale have now both left the club, along with the rest of Yorkshire’s coaching team.
Moxon had served as Yorkshire’s director of cricket since 2007, while Gale took the first XI coaching reins from Jason Gillespie in 2016, having spent the previous seven years as Yorkshire captain.
“We can confirm that Martyn Moxon, Director of Cricket, and Andrew Gale, First XI Coach, have left the Club today (3 December), in addition to all members of the coaching team,” Yorkshire said in a statement on Friday.
“A new Director of Cricket will be appointed imminently, alongside a new coaching team which is being recruited.
“The backroom medical team, external services provided by Pavilion Physiotherapy Clinic, has also left the Club. An interim medical team is also in the process of being appointed.
“We thank everyone who is leaving for their service. Further announcements will be made in due course.”
Yorkshire’s new director and chairman, Lord Kamlesh Patel of Bradford, said the changes were in the best interests of the club as they look to move forward and try to re-establish trust in the wake of the Rafiq allegations.
“Significant change is required at Yorkshire County Cricket Club and we are committed to taking whatever action is necessary to regain trust,” he said.
“The decisions announced today were difficult to make, but are in the best interests of the Club. Without making important changes to how we are run, we cannot move on from the past to become a culture which is progressive and inclusive.
“We want to make Yorkshire County Cricket Club a place for everyone, from all backgrounds. To do this, we need to rebuild our culture and instil positive values in everyone associated with Yorkshire. We are determined to learn from the mistakes of the past to become a Club which people can trust.
“We are hoping to announce a new Director of Cricket in the coming days. We have a huge rebuilding job to do but we are confident that this heralds a step forward towards a brighter future”.