Mount has signed a contract until the end of the 2027-28 season with the option of a further year.
ESPN reported last week the two clubs had agreed a deal worth £55 million ($69.5m) with another £5m ($6.3m) in add-ons.
Sources told ESPN the bonuses due to Chelsea are “strongly dependent” on appearances as well as Mount’s success at Old Trafford.
“It’s never easy leaving the club where you grew up, but Manchester United will provide an exciting new challenge for the next phase of my career,” Mount said in a statement.
“Everyone can see that the club has made big steps forward under Erik ten Hag. Having met with the manager and discussed his plans, I couldn’t be more excited for the seasons ahead, and am ready for the hard work expected here.”
The 24-year-old, who had one year remaining on his Chelsea contract, is United’s first signing of the summer transfer window.
United football director, John Murtough, said: “Mason is an extremely intelligent footballer and has so many fantastic technical qualities that will significantly add to our squad.
“We have admired his talents for a long time, so we are delighted that he has chosen to take the next steps in his career here at Old Trafford.”
Man United sign Mason Mount from Chelsea in £60m deal