The Serbia international completed a £40m switch to the Red Devils from Premier League champions Chelsea on Tuesday evening.
Matic will be tasked with reinforcing the Manchester United midfield and protecting the defence alongside Marouane Fellaini and Ander Herrera.
The 29-year-old’s addition should also free up Pogba to focus on creating more assists and goals for the Manchester United team this season.
The France star was criticised last term following a muted start to his second spell at Old Trafford under Jose Mourinho.
The Red Devils signed Pogba in a world-record £89m deal from Serie A champions Juventus last summer.
However, the versatile midfielder scored five goals and made four assists in 31 appearances in the Premier League campaign.
Former Southampton star Le Tissier wants to see more from Pogba in the 2017-18 season following the addition of Matic.
“After signing Nemanja Matic I’m excited to see how Paul Pogba does, with a bit more freedom to operate in a more advanced position,” Le Tissier told Sky Sports.
“I’d like to see him take games by the scruff of the neck and show everybody why he’s worth the £89m paid for him.”
Pogba scored Manchester United’s opening goal in a 2-0 win against Dutch giants Ajax in the Europa League final.
The Red Devils have also signed Swedish defender Victor Lindelof and Everton striker Romelu Lukaku in the summer transfer window.
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