If Matic plays regularly for Jose Mourinho's side, Giggs believes that it will allow Pogba to move further up the pitch and create more of an impact.
The France international returned to Old Trafford from Juventus last summer in an £89m deal, making the midfielder the most expensive footballer in history.
"I expect Pogba will improve a lot this season," talkSPORT quotes Giggs as saying. "He's been back a year now and the introduction of Matic is a good buy because it frees him up.
"That's what you want to see from Pogba, getting on the end of crosses and scoring goals. I think he's capable of dropping deep or playing in an old-fashioned midfield two but he can get further forward and I expect him to be more effective this year."
Pogba scored nine goals last season.