Since joining the Toffees from Standard Liege in 2008, the Belgian has become one of the most accomplished midfielders in the Premier League playing under new United boss David Moyes.
He revealed that the lure of Champions League football and the prospect of adding to the Jupiler League title he won with Liege ultimately drove his decision to leave Merseyside.
"I know Everton wanted to keep me but I played with them for five years and it was time to leave," the 25-year-old told Sky Sports News.
"I want to thank Everton for supporting me but it's a new story for me now. I want to win the trophy, play Champions League and with United I can do that."
Fellaini has linked up with the Belgium squad ahead of their World Cup qualifier against Scotland on Friday.