Mount has signed a contract until the end of the 2027-28 season, with the option of a further year.
ESPN reported last week that the two clubs had agreed on 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.”
Mount, 24, 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.”
Mount issued a message to Chelsea supporters on Tuesday as he said farewell to the club.
“I feel you deserve more than a written statement so I wanted to tell you directly how grateful I have been for all of your support over the last 18 years,” he wrote on Instagram.
“I know some of you won’t be happy with my decision, but it’s what’s right for me at this moment in my career.”