The Red Devils have signed Matic, Victor Lindelof and Romelu Lukaku as part of Jose Mourinho's United summer reinforcement drive.
The 29-year-old helped Antonio Conte's Chelsea win the Premier League last season and was an influential player in Mourinho's victorious side at Stamford Bridge in the 2014-15 campaign.
Matic is now ready to make an impact at United and is expecting a successful season at Old Trafford. He said, "We have to rest well because we have a very important game on Sunday against West Ham."
"It's the start of the Premier League and it's very important for us. As you know the Premier League is the main target. There is a lot of games, it's a long season but I expect us to do well."
The Serbian played the full 90 minutes of Tuesday's 2-1 Super Cup loss to Real Madrid, but believes his side performed well against the Spanish and European champions.
Matic added, "I think we played everything so we don't lose this game. We played against a very good side. Very experienced. They know how to play these games."
"We are not happy that we lost but did everything. We had an opportunity to equalise, Marcus (Rashford) had a good chance and didn't score, unluckily for us, but this is football."