With the clock ticking down to the 11pm deadline, Fellaini handed in a transfer request at Everton in an effort to force through a deal.
He got his wish as United wrapped up an agreement with just minutes to spare.
Fellaini is now looking forward to taking on a new challenge at Old Trafford and believes he is linking up with a squad that is capable of defending its Premier League title.
The Belgium international told Sky Sports after playing 68 minutes for his country in a 2-0 victory over Scotland on Friday: "It was a great week for me. It was nervous on Monday, but I have my transfer and I won with Belgium, so I'm happy.
"When I started the campaign with Everton, I looked forward for a transfer and in the end I am happy.
"I look forward to playing with the players. I need to work hard for my place. I want to win something with Manchester. I want to play a lot of games and win a trophy.
"It will be tough, every year it is tough for the big teams. But I think Manchester United have quality to win the trophy. I look forward to this.
"It's a big step for me. But I have played for 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."