The England midfielder has signed a £250,000-a-week contract at Old Trafford until 2028 for a reported £60million fee.
Mount previously announced the end of his 18-year association with the Blues via social media on Tuesday.
"Given the speculation over the last six months this may not come as a surprise to you, but it doesn't make it any easier to tell you that I've made the decision to leave Chelsea," Mount said in a farewell message to Chelsea fans on Instagram.
"I feel you deserve more than just a written statement, so I wanted to tell you directly how grateful I've been for all of your support over the last 18 years.
"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.
"I joined Chelsea when I was six years old and we've been through a lot together."
United first teased a video of Mount putting on a Red Devils shirt with the caption: "The excitement is mounting."
Sources say Mount was manager Erik ten Hag's top transfer target this summer, with the club keen to reinforce their attacking threat in midfield.
Speaking on the club's official website, Mount said: "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.
Having competed against them, I know just how strong a squad it is that I'm joining, and I can’t wait to be part of this group's drive to win major trophies.
"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.
"I am hugely ambitious; I know how amazing it feels to win major trophies and what it takes to do it. I will be giving everything to experience that again at Manchester United."
John Murtough, Manchester United football director, added: "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.
"His style of play and attributes are a perfect fit for this squad, and we all believe that he will only improve further working with Erik ten Hag and his coaching staff.
"Mason himself is a world-class player but he also has the ability to improve the players around him through his game intelligence and tactical awareness.
"We were particularly impressed by his strong desire to join United, and his thirst for further success, as we push to drive up our performance levels next season and beyond."
He has spent his entire career at Chelsea, with loan spells at Derby and Vitesse during his earlier years.
Mount made 279 club appearances, scoring 58 goals and contributing 53 assists, and played an integral role in Chelsea's run to Champions League glory in 2020/21. He also won Chelsea's Player of the Year award that season and the following campaign.
He has 36 caps for England and played a key role in his country’s run to the European Championship final in 2021.
However, his form dipped last year under Graham Potter and caretaker manager Frank Lampard, with the attacking midfielder struggling to break into the side amid a plethora of fresh signings under the club's new ownership.
