The Scotsman has claimed that he wants to get the Belgium international involved in the team "quite quickly" following his arrival from Everton for £27m on deadline day.
"[I'm] very pleased," Moyes said in a press conference. "When I brought him to Everton from Standard Liege, he was someone who not many people knew an awful lot about.
"He is effective in different areas of field. If he keeps improving as he has done, we could have a really top player on our hands.
"It's been interesting watching him train this week. He's not out of place though. We will get him involved quite quickly."
Moyes also revealed that Fellaini's arrival was late because the club were trying to sign the midfielder's teammate Leighton Baines, who is expected to be offered a new contract at Everton.