The 25-year-old midfielder joined the Toffees on a free transfer from Manchester United earlier this summer and Martinez was delighted with the way he has performed since his arrival.
Martinez already rates Cleverley in his top echelon of leaders and expects the former Aston Villa loanee to have a big influence on the playing group at Goodison Park.
"I always mention our biggest strength is our dressing room as a football club, that core we have from our captain Phil Jagielka, to Tony Hibbert, Tim Howard, Leon Osman and Leighton Baines," said Martinez after Everton defeated Stoke City on penalties in the Barclays Asia Trophy on Wednesday.
"They are players who allow you to come in and as long as you get real high standards, you are always welcome.
"And I think Tom is a real example of that. He had a good connection with the England footballers, but straight away he has adapted really well in the way of working and playing, and you can see that he has terrific Premier League experience."