The Serbian international has penned a three-year deal at Old Trafford that includes the option of an additional 12 months and arrives for an undisclosed fee believed to be an initial £40m ($52.4m) that could rise by a further £5m with add-ons.
"I am delighted to have joined Manchester United," Matic said. "To work with Jose Mourinho once again was an opportunity I couldn't turn down.
"I have enjoyed my time at Chelsea and would like to thank the club and the fans for their support. I cannot wait to meet my new team-mates and to start training with them.
"This is a very exciting time for the club and I am looking forward to playing my part in creating more history for this great club."
Mourinho had made no secret of his desire to add a new central midfielder and winger to his squad following the respective additions of versatile defender Victor Lindelof and striker Romelu Lukaku.
However, he feared that he might have to settle for just one further addition during a particularly manic window amid mounting pressure on executive vice-chairman Ed Woodward.
The self-proclaimed 'Special One' was also keen on Eric Dier, although Tottenham Hotspur, still yet to make a single signing so far this summer, have remained steadfast in their desire not to lose another key first-team player following the £50m sale of Kyle Walker to Manchester City.
Matic is a midfielder that Mourinho knows very well indeed. He was the man responsible for bringing the 28-year-old back to Chelsea in a £21m deal in January 2014, three years after he had been sold to Benfica as part of the transfer that saw David Luiz move to Stamford Bridge for the first time.
The former Vitesse Arnhem loanee made a total of 154 appearances during his two separate stints with the Blues, including 36 during the 2014-15 title-winning season under Mourinho.
He featured 40 times last term to help resurgent Chelsea win the Premier League for the second time in three years, but was left out of Antonio Conte's squad for a pre-season tour of the Far East amid those links to United.
"Nemanja is a Manchester United player and a Jose Mourinho player," Mourinho said. "He represents everything we want in a footballer; loyalty, consistency, ambition, team player.
"I would like to thank him for his desire to join us because without that, it would be impossible to have him here. I am sure our players and supporters will love him. A big welcome to our new number 31."
Matic underwent his medical at Carrington on Sunday (30 July) and was promptly pictured on social media donning a United training top. He will hope to make his debut for his new club on Wednesday as United face Serie A outfit Sampdoria at Dublin's Aviva Stadium, six days before the Europa League holders battle Real Madrid in the Uefa Super Cup in Skopje.
Mourinho's side open the 2017-18 top-flight campaign at home to West Ham United on 13 August.