Matic, 29, c ompleted a move reported to be worth £40 million to reunite with manager Jose Mourinho at Old Trafford.
The Serbia international gives United extra options in midfield, where they already boast the talents of Ander Herrera, Paul Pogba and Marouane Fellaini among others.
And having worn the No. 21 jersey at Stamford Bridge, Matic will pull on No. 31 when he makes his Red Devils debut.
A photo published on Twitter by sponsors Adidas confirmed the switch, as Herrera wears 21 currently at Old Trafford.
Mourinho also made reference to his number upon presenting the new signing: "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."