"Yeah, I think everybody has to be given the chance to [flourish at United]," Moyes told MUTV. "I'm confident he can.
"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.
"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."
United have reportedly paid £27.5m to Everton for Fellaini's services.