The powerful Belgium international enjoyed a superb season on loan at the Toffees last term and finished as their top scorer with 15 goals.
The Blues made the loan stay permanent when they signed Lukaku from Chelsea for a whopping £28 million and a lot will rest on the shoulders of the youngster if Everton are to attain a spot in the top four this season.
Everton have also signed Muhamed Besic, Brendan Galloway and Gareth Barry, while Christian Atsu has joined on loan from Chelsea, but it is the signing of Lukaku that has got pulses racing at Goodison Park.
The swashbuckling Lukaku was a huge hit on Merseyside last term and the signing was a massive statement of intent from a side that has continually been forced to fight for a place at higher end of the Premier League on a shoestring budget.
Martinez's side host Arsenal this Saturday evening, and ahead of the tie, the Catalan has talked up the talents of his marquee signing.
He told the Liverpool Echo: "He’s a complete player and very mature for such a young age. He knows what he brings to the side but can also adapt his way of playing just to suit the team and the opposition."
"That’s why he is ahead of a lot of other strikers in the world. As a runner with the ball he can be a strong footballer, he has the hold-up play and can be a top finisher and use space well."
"Then more importantly he can take instructions in with a real understanding and precision like that game."
The Saturday evening game gives both teams an early test of their pre-season aspirations at Goodison Park.
The Blues are looking to stake an early claim for their Champions League hopes, while Arsenal have designs on winning the Premier League.