The two are international team-mates for Belgium and, having played together for several years, the Scot decided to seek his midfielder's opinion before making his move.
The 24-year-old was signed by the Goodison Park club ahead of their opening game of the season at home to Manchester United, but the move took place after the registration deadline for Monday's night's game, so instead he will be paraded in front of the fans rather than challenging Croatian striker Nikica Jelavic for a starting spot.
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"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."
As well helping his manager during the transfer, Fellaini was also in contact with Mirallas, and advised him that a move to Goodison Park would be a good move for his career.
"I said welcome to the Premier League because it is difficult to get a move to the Premier League," Fellaini added. "I told him to enjoy it because it is a special league.
"I think it's good for Everton because he's a good player and we need more players for the squad. I hope he scores a lot of goals for Everton and gets some assists too.
“He's clever, he's a good guy and I think the team will take him into the group quickly. He will be happy here."