The 24-year-old has been heavily linked with a move to the Red Devils in recent weeks, but the club had been left frustrated in their negotiations with their Premier League rivals.
Chelsea are said to have rejected a £55m offer from Man United earlier this week, but there have since been fresh discussions between the two clubs over a deal.
According to Italian journalist Fabrizio Romano, an agreement has now been reached between the two clubs, with Man United agreeing to pay £60m to purchase the England international.
Romano claims that the Red Devils will pay a fixed fee of £55m plus £5m in add-ons, with the club refusing to meet Chelsea's £65m valuation of the versatile playmaker.
Mount's contract at Old Trafford will allegedly be valid until June 2028, with the two parties agreeing personal terms 'weeks ago'.
The Chelsea academy product is expected to undergo a medical with the 20-time English champions after the weekend before an announcement is made over his move to Manchester.
Man United had also been linked with Declan Rice, but the West Ham United captain is on the verge of moving to Arsenal, and Red Devils head coach Erik ten Hag is said to have always viewed Mount as his leading target in that area of the field.
The Englishman's versatility is said to have appealed greatly to Ten Hag, as he is capable of featuring in central midfield or further up the pitch.
Mount found it difficult to make his mark for Chelsea during a turbulent 2022-23 campaign, but he did struggle with injury problems and missed the end of the season following a pelvic operation.
The attacker will leave the Blues having made 195 appearances in all competitions, scoring 33 goals and contributing 37 assists in the process.
Mount has managed three goals and eight assists in 35 Champions League outings, with Man United preparing to return to Europe's leading cup competition next term.
Meanwhile, the Englishman has featured on 129 occasions in the Premier League, scoring 27 goals and registering 24 assists in the process.
Mount is set to become Man United's first signing of the summer transfer window, but the Red Devils also want to bring in a centre-forward, while at least one goalkeeper will arrive before the market closes.