The midfielder completed a deadline-day move to the Premier League champions for £27.5m.
The Belgian, who left Everton after five years with the club, does feel, however, that he will be able to cope with the demands of playing for the Red Devils.
"It is a big step for me. But I have played five years in England, I know the league and I know the players so I don't think I will have a problem with this move," he told The Mirror.
"Of course I look forward to it, I am playing with big players so I need to work hard for my place."
Fellaini also said that despite the protracted negotiations, he is happy to have finally made the move.
"I was a little bit nervous on Monday but in the end I have my transfer and I have won with Belgium so I am happy," he added.
Fellaini played in Belgium's 2-0 win against Scotland last night.