Matic, who turns 29 on Tuesday, has signed a three-year contract with the option of an additional year after he completed a medical at the club’s Carrington training complex on Sunday.
He said: “I am delighted to have joined Manchester United. 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 added: “Nemanja is a Manchester United player and a Jose Mourinho player. 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.”