A picture of Matic in United training kit with the number 31 on – vacated by Bastian Schweinsteiger last season when he moved to Chicago Fire – did the rounds on social media on Sunday, with the caption "first hand information" written in Serbian, before the club confirmed the news on their own Twitter account on Monday.
It is the second time Jose Mourinho has signed the Serbian as the club take their summer spending nearly £150m following the arrivals of Romelu Lukaku and Victor Lindelof earlier this summer.
Mourinho said: "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."
Matic 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 had seen bringing in a defensive midfielder as his main priority after bolstering both his defence and attack and he wanted someone he knew he could trust to understand what was asked of him from the get-go.
United had felt that Chelsea would refuse to do a deal due to both the hijacking of their bid for Lukaku from Everton and the belief they would be strengthening a rival, but the champions’ recent progress in the market meant the move was finally given the green light.
Juventus and Internazionale wanted Matic too but the Serbian’s relationship with Mourinho meant that Old Trafford was his first choice.
United had also been linked with Monaco’s Fabinho for the position, although Mourinho sees him more as a full-back, while their interest in Eric Dier hit a brick wall after finding Tottenham Hotspur “impossible” to deal with.
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