The Brazilian star has arrived at Old Trafford after spending the pre-season with his former side.
Casemiro is planning to work hard in training to keep up with the physical demands of the Premier League.
The five-time Champions League winner left Real Madrid to join Manchester United on a £70 million deal last week.
Following a glorious seven-year spell at Santiago Bernabeu, Casemiro feels he is ready for a new adventure in the English top-flight.
“Well, I think that English football is very physical and, without doubt, it’s very tough,” he told Man Utd’s official website.
“But what I like most about the players, the referees, the fans in this country is that they are fair, regardless of how physical things may be, everyone is fair.
“Of course there’s contact in football, clashes. But the fairness with which it’s played in this league is the most beautiful thing.
We know it’s a competitive league, whether you’re playing home or away, every game is very tough.
“All of the teams are equal and I think it’s not just those teams who play in the Champions or Europa League, the top team can lose to the bottom one and that is what the league is like.
“It’s beautiful that it is so competitive and I’m excited to be playing in it.”
Casemiro made two pre-season appearances for Real Madrid before completing his move to Old Trafford.
The midfielder could make his Man Utd debut when they take on Southampton on Saturday.