United will pay an initial £55 million ($69.4m) with another £5m ($6.3m) in add-ons.
Sources told ESPN the bonuses due to Chelsea are "strongly dependent" on appearances and Mount's success at Old Trafford.
Sources added that, with Mount currently on holiday, his medical with United is set to take place next week.
The two clubs have reached a compromise after Chelsea originally demanded £70m for the England international. United have seen bids of £40m, £50m and £55m rejected by Chelsea.
Mount, 24, was set to enter the final year of his contract at Stamford Bridge and negotiations over a new deal had collapsed. Had he stayed at Chelsea, he could have left as a free agent next summer.
He will become manager Erik ten Hag's first new signing of the summer.
Mount leaves Chelsea having made 195 appearances for his boyhood club. He was part of the team which won the Champions League under Thomas Tuchel in 2021.
Mount, who has agreed personal terms with United, will next undergo a medical and will be part of Ten Hag's squad for the preseason tour of the United States, which begins in New York on July 20.
He could make his United debut in a friendly against Leeds United in Oslo on July 12.