The 41-year-old joined the Club ahead of the 2017/18 campaign and quickly became an integral part of the first-team coaching staff, but has opted to move on to pastures new due to family reasons.
Speaking about his departure, Mountain added: “I have to say that I was made very welcome by everyone connected with the Club, and by the people of Hull, from the moment I arrived.
“I have had the pleasure of working with a fantastic group of people here and the friendships formed during my short time at the Club have made this a very difficult decision, but it is one that I have had to make for the sake of my family.
“I would like to take this opportunity to wish Nigel and the team every success going forward and thank everyone at the Club for their support during my time here.”
Head Coach Nigel Adkins added: “We’re all sad to see Pat leave, but we understand his reasons for doing so. Pat has made a big contribution during his seven months here and is a popular figure with everyone at the Club and he leaves with our best wishes.”
The process to recruit a new Goalkeeping Coach is underway.