The Belgium international midfielder's future had been the subject of intense speculation throughout the close-season, but it took until the final day of the transfer window on Monday before his switch to United materialised.
The Premier League champions paid £27.5 million for the former Standard Liege man and he is confident that he will not have any problems fitting into the squad as he links up once again with David Moyes.
The 25-year-old, who helped Belgium beat Scotland 2-0 on Friday in a FIFA World Cup qualifier, said: "When I started the campaign with Everton, I looked forward for a transfer and in the end I am happy.
"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.
"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.
"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 championship. I look forward to this."
Get the best features, fun and footballing frolics straight to your inbox every week.
Thank you for signing up to Four Four Two. You will receive a verification email shortly.
There was a problem. Please refresh the page and try again.