The 25-year-old had been linked with the title holders for weeks before the window slammed shut, but the deal was only announced after it had closed on Monday.
Fellaini, who scored 11 goals in 31 league appearances for Everton last season, sees him reignite his working relationship with Moyes, who replaced Alex Ferguson at Old Trafford in May.
The midfielder's arrival marked just the second addition for United during the window, after Uruguay youth international full-back Guillermo Varela.
But Fellaini has immediately targeted trophies after completing his move in a deal worth £27.5 million.
"I am thrilled to sign for Manchester United," he told the club's official website.
"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."
He will now link up with the Belgium squad for their FIFA World Cup qualifier against Scotland on Friday before potentially making his United bow against Crystal Palace on September 14.
Moyes was also delighted to have sealed the deal for Fellaini and believes he will make a big impact on the champions' squad.
He added: "I have worked with Marouane for five years and I’m delighted he has decided to join Manchester United.
"He is a player with great ability and strength and I think he will make a real difference to our squad."
