Fellaini moved to United for £27.5 million.
Moyes told manutd.com: "He's a very good footballer and a good technician. He has the ability to score goals and play in several different positions in the midfield. I think that's an area where everybody felt we could do with strengthening. He'll give us different options in different games in terms of where we can use him.
"He's still young and improving. For me, he's been one of the best midfielders in the Premier League over the last few seasons. If he can join a club like Manchester United and continue to improve hopefully we'll have a real good player on our hands.
"I think he's a talented boy. He has a good mentality, he's a good professional. We're looking forward to seeing how he does.
"He helped me over the years in different ways. 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."
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