The 24-year-old striker completed his move from Olympiakos to Goodison Park on Sunday for a fee in the region of £6m.
Fellaini and Mirallas are good friends from the Belgium national side, and the former says that Moyes asked for his opinion when considering a move for the forward.
"Last week or two weeks ago he (Moyes) asked me what I thought about him," Fellaini told the club's official website. "I told him he was a good player, a good dribbler, he's quick, a good finisher and I said I hoped he could come here because he could help the team.
"He can keep the ball, take people on, cross the ball, score goals, so I think he will be good for the team.
"He's a quick player, with good technique, good dribbling ability, last year he was top scorer [for Olympiakos] and I think he is a player who will excite the fans. I hope so."
Everton start their Premier League season on Monday night when they host Manchester United.