Matic was one of Mourinho's favourite players during the Portuguese's second stint as Chelsea boss.
Matic was one of Mourinho's favourite players during the Portuguese's second stint as Chelsea boss, winning the Premier League title together in 2015.
The 29-year-old midfielder was left out of Chelsea's squad for their pre-season tour of China as there was no place for him in the team following the signing of Tiemoué Bakayoko from Monaco.
Chelsea's loss, however, is Mourinho's gain as the manager describes the midfielder as a player that 'represents everything we want in a footballer'.
"Nemanja is a Manchester United player and a Jose Mourinho player. He represents everything we want in a footballer; loyalty, consistency, ambition, team player," Mourinho told Manchester United website.
"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 is excited with joining his former coach Mourinho who brought him back to Chelsea in January 2014.
"I am delighted to have joined Manchester United. To work with Jose Mourinho once again was an opportunity I couldn't turn down," the midfielder said.
"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."
Matic could make his first Manchester United appearance in a pre-season friendly game against Sampdoria in Dublin on Wednesday, August 2.