The 25-year-old joined the Merseyside outfit on a free transfer - following a season-long loan at Villa Park from Manchester United - this summer and signed a five-year-deal.
Following Cleverley's displays in the Everton's opening pre-season fixtures, versus Swindon Town and Stoke City, Martinez is delighted with the ease in which the midfielder has made the transition into his squad.
The Blues boss told the Liverpool Echo: “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.”
“But he’s added something different and all we want is to keep adding.”
What do the stats say?
Cleverley made 31 appearances for Aston Villa last season, scoring three goals and fashioning 36 key passes - the fourth highest total at the club. However, while his output in the final third was impressive, it is not his scoring or creative instincts that the Englishman is renowned for.
Rather, he is highly-valued by Martinez for his concentration and composure in possession - this is also displayed in the statistics. Last term, for example, he completed a higher percentage of his total attempted passes (86% completion rate) than any first-team player at Goodison Park, while he also found success in 50% of his take ons.