Moyes was relieved of his position as United manager on Tuesday, less than 12 months into a six-year contract, with United languishing in seventh place in the Premier League and unable to qualify for next year's UEFA Champions League.
Club legend Ryan Giggs has taken over as interim manager at Old Trafford, assisted by former team-mates Paul Scholes, Nicky Butt and Phil Neville.
A statement on the League Managers Association's website on Friday confirmed that United and Moyes had come to an agreement.
"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," the statement read.
"A settlement agreement is in the process of being finalised.
"No further comment will be made in relation to this issue."
