United had made a joint bid of £28m for both Fellaini, 25, and full-back Leighton Baines in August, which the Toffees had described as "derisory".
Fellaini had a release clause of £23.5m in his Everton deal until 31 July.
Manager David Moyes said: "He is a player with great ability and strength and I think he will make a real difference to our squad."
He added: "He can play higher up, if we need it, behind the striker or as a defensive or holding midfielder. In any position in the middle of the field he's comfortable.
"Because of that I think it's definitely a position where people have said we've been short of numbers, with the likes of Paul Scholes [retiring] and Darren Fletcher not ready to come back just now. I felt we needed to strengthen there and I'm glad we got him."
The Belgian, who joined Everton from Standard Liege for £15m in 2008, was contracted to the Toffees until 2016.
He 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.
"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."
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