Having previously helped Jose Mourinho to land the Premier League title at Stamford Bridge, the Serbian midfielder has been reunited with the Portuguese at Old Trafford this summer.
He has settled quickly into new surroundings, with a Man of the Match performance helping United to make a dream start to their 2017-18 campaign with a 4-0 mauling of West Ham on Sunday.
Matic is delighted with how things are going and believes that, having signed a three-year contract, he could take in a lengthy spell with the Red Devils.
The 29-year-old told MUTV: “Thanks to the guys, they have accepted me from my first day and I feel
“Thanks to them, I feel very comfortable and I feel like I will be here a long time. They have helped me, and I am happy if I give them something back, and that I helped us to win.
“We played good football, and I think our supporters enjoyed it as well. It’s good to start well with three points, the season is long but we have to collect a lot of points and we’ve had a good start.
“It was great [to play at Old Trafford], when you wear that [United] shirt you feel some kind of pressure because this is a big club, but that’s why we are here.
“We know that it’s a big responsibility to play for Manchester United and I’m happy that we have started well and that I hope we continue like this - I’m sure this group can do good things.”
Matic was not the only United new boy to impress on his Premier League bow, with £75 million striker Romelu Lukaku bagging a brace against the Hammers.
“I am happy for him – not only that he scored goals – but his amazing all-round game as well,” Matic said.
“He saved a lot of balls and he gave us self-confidence up front.
“It was very important for us that he scored his first two goals and, after that, it was easier for us to play, the game was more open, and there was more space to use. I’m happy for him and that we have him on the team, and I’m sure he will continue his form.”
United will be hoping for more of the same in their next outing against Swansea, with Mourinho’s men then set to discover their Champions League group stage opponents on August 24.