Successors will be appointed "imminently" announced the county after clearing out of the entire Yorkshire coaching team.
Since November 9, stress-related illness had Moxon signed off, whilst Gale was suspended due to pending disciplinary hearing into a historical social media post.
Their departures follow those of club president Roger Hutton, who stepped down on November 5, and chief executive Mark Arthur, who resigned a week later following widespread condemnation of Yorkshire over its handling of a racism investigation and the treatment of former player Rafiq .
Moxon, 61, was an opening batsman for Yorkshire from 1980-97 and returned to become director of cricket in 2007.
Gale, 38, was also an opening batsman and captained the team until his retirement at the end of the 2016 season when he was appointed as coach.
Both were heavily criticised at the Department for Culture, Media and Sport hearing at Westminster while Rafiq repeated his call for Arthur and Moxon to step down from their roles at the club.
"I don't think Martyn and Andrew can (continue)," Rafiq said a month ago. "I don't think it's possible for Yorkshire to move forward with them in there, with them knowing full well what role they played in that institution."
Yorkshire say the total number of departures is 16, including six members of the backroom medical team provided by Pavilion Physiotherapy Clinic, and that an interim medical team is in the process of being appointed.
Lord Patel, Yorkshire chair, said: "Significant change is required at Yorkshire County Cricket Club and we are committed to taking whatever action is necessary to regain trust.
"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."