The 25-year-old is training with his Belgium team-mates as they prepare for Friday's World Cup qualifier in Scotland as he continues to reflect on his dramatic move to United minutes before the transfer window closed.
Having arrived at Goodison Park in September 2008 from Standard Liege for £15m, Fellaini was an integral part of Everton's success but opted to hand in a transfer request late on Monday and eventually secured a deal with the Premier League champions worth £27.5m.
"I know Everton wanted to keep me but I played with them for five years and it was time to leave," the attacking midfielder 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."
It was a frantic deadline day for United as their failed attempts to secure the services of Athletic Bilbao's Ander Herrera and Real Madrid's Fabio Coentrao ended more fruitfully with the deal for Fellaini.
United boss David Moyes was full of compliments for the player he managed at Everton, saying: "He has attributes other people don't have. And with those qualities he has, I am sure he will be a big player for Manchester United."
When asked about the rushed nature of his transfer, Fellaini added: "It was last minute, last second. It was difficult but now I'm happy and now I concentrate for Friday.
"It was busy but now I'm here I can rest. I don't have the press and I'm happy to be here. Football is like this. The transfer window is like this. The most important thing is I am here. It's OK now."
And on the prospect of helping his new team to successfully defend their Premier League crown, he said: "I hope. I will do everything."
Meanwhile Everton have denied reports waived bonuses accounted for £4million of his transfer fee.
The reports suggested his transfer request saved Everton £4m in bonuses, allowing them to accept an offer of £23.5million from United in line with an expired buy-out clause in Fellaini's contract.
But Everton's director of communications Alan Myers has shot down those suggestions, insisting the £27.5million for Fellaini is coming solely from the old Trafford vaults.
Myers wrote on his Twitter page: "For those asking: No Felli did NOT pay £4m of the transfer fee! The buying club will pay £27.5m."
The fee for Fellaini is understood to be £26.5m up front with a further £1m in add-ons, some of which Everton forked out on deadline-day to sign James McCarthy and bring in Gareth Barry and Romelu Lukaku on loan.