It was just after 2am on Tuesday morning, three hours after the transfer window closed, that United confirmed the £27.5million deal had finally been done.
Belgium international midfielder Fellaini follows Moyes from Goodison Park to Old Trafford having first linked up with him in September 2008, when he joined Everton for an initial fee of £15million from Standard Liege.
"I have worked with Marouane for five years and I'm delighted he has decided to join Manchester United," said Moyes.
"He is a player with great ability and strength and I think he will make a real difference to our squad."
The 25-year-old had a £23.5milion release clause in his Toffees contract but that expired on 31 July. With Moyes having allowed that to lapse, United have ended up paying £4million more for his services.
The Fellaini fee is the fourth highest transfer in United's history, ahead of Wayne Rooney and behind only Dimitar Berbatov, Rio Ferdinand and Juan Sebastian Veron.
His 12 goals for Everton last term underline the goal threat he can provide given, other than Shinji Kagawa, who scored six times, no midfielder managed more than two strikes for the Red Devils last term.
After securing his move, Fellaini said: "I am thrilled to sign for Manchester United.
"I have known the manager for many years now and I have a lot of respect for his way of working.
"When I was given the opportunity to work with him again, I jumped at the chance.
"I had a fantastic time at Everton and I'd like to thank all the fans and staff there for everything they have done for me.
"But being a Manchester United player is something that every player dreams of and I believe that I can make a real contribution to the team's efforts to win trophies in the future."
Fellaini, who also tweeted his appreciation to Everton fans, will now link up with the Belgium squad ahead of their World Cup qualifying Group A match against Scotland at Hampden on Friday night.
He is set to make his United debut in the Premier League clash at home to Crystal Palace on Saturday, September 14.
It will be very interesting to see how exactly Moyes utilities Fellani as he was played almost entirely out of position every week under Moyes at Everton. Its shameful we got more for this fella than we did for Rooney, we have our dope of a chairman and Moyes to thank for that but we have got rid of one of them, cant wait til Bill follow suit.- boggo