The Scot, who only signed a six-year contract last summer, was axed from his post at Old Trafford on Tuesday.
A statement from the League Managers Association (LMA), the body that looks after the interests of managers, read: "The League Managers Association and Manchester United are pleased to confirm that terms of settlement have been agreed between the club and David Moyes in respect of the termination of his employment.
"A settlement agreement is in the process of being finalised. No further comment will be made in relation to this issue."
There was no indication how much money Moyes had received as part of the severance deal.
United veteran Ryan Giggs will take charge of the club for the season's final four games, starting on Saturday against Norwich, live on Sky Sports 1HD, after being handed interim control of the team.
The LMA expressed its dissatisfaction at the way Moyes' departure was handled by United with his imminent departure widely reported 24 hours before it was officially announced.
LMA chief executive Richard Bevan said on Wednesday: "Throughout his time at United, David, as he always does, has conducted himself with integrity and professionalism, values that he believes in and that have been strongly associated with the club and its rich tradition.
"It is therefore sad to see the end of David's tenure at United being handled in an unprofessional manner."
A United spokesman denied any wrongdoing and said: "We do not accept that it was handled in an unprofessional manner."