Murtaugh has spent the past 11 years at the Old Trafford club, arriving when David Moyes took over from Sir Alex Ferguson as manager.
He has since been promoted to several different roles, without achieving much success in any area.
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Sir Jim Ratcliffe, co-owner of United, said in a statement: "We want to thank John for his loyal service over many years, and for his support and integrity during this period of transition.
"He leaves with our best wishes for the future."
Joel Glazer, co-chairman of United, added: "After 11 years of tireless work for the club, John has mutually agreed with us that now is the right time to step aside and allow the new football leadership structure to be put in place.
"He will always be welcome back at Manchester United as a friend of the club."