The midfielder spent three-and-a-half years in his second spell at Chelsea, winning the Premier League twice in that time before moving to United ahead of this season in a reported £40 million move.
Matic was named man-of-the match in his Premier League debut as Jose Mourinho's men impressively beat West Ham 4-0 last weekend.
He is loving life at United and risked the ire of his former club's fans by claiming he was in no doubt his new side were bigger.
Asked if United were the biggest club he has played for, Matic told Sky Sports: "Definitely, everyone knows what Manchester United is about.
"When you say Manchester United, it is different.
"When I came here for the first day, I could feel that the people at the club help you every day if you need something and supporters are very important for this club.
"After every training session, they are waiting for us outside the training ground to take pictures, to give a signature so I think the club is one of the biggest in the world.
"Maybe you have two or three clubs similar to United, but Manchester is one of the biggest clubs in the world for sure."
Matic revealed it was an easy decision to join a club of United's stature, particularly given it was his former boss who Mourinho came calling.
"He was very important for me," Matic said of Mourinho.
"He bought me to Chelsea from Benfica and now when I decided to come to Manchester, he was a reason to come here.
"Mourinho was the reason and so was the club, Manchester United, so you don't need to think a lot about if you are going to come.
"My decision was very quick and very clear."