The Toffees swooped for Lukaku's services on transfer deadline day, taking him on a season-long loan deal from Chelsea.
At just 20 years of age, the Belgium international still has much to learn.
He has, however, already shown - during a spell at West Bromwich Albion last season - that he is capable of terrorising Premier League defences, and Martinez is expecting more of the same from Lukaku in 2013/14.
He told evertontv: "He's still a young man but he's got everything.
"It's going to be really exciting to see Romelu developing and growing and if he can do that in an Everton shirt, he's going to bring a lot of smiles to all our fans. It's an exciting period for everyone."
Martinez added on a striker who is currently readying himself for World Cup qualifying duty: "What he's achieved already is impressive. Probably the biggest point is that we all feel it is time to kick on and carry on achieving.
"He had a massive move at a very young age and we all know what he's capable of doing in the Barclays Premier League.
"He's not someone that hasn't had an impact in the league; he's someone that, at just 20-years-old, has huge potential. He's part of a very talented generation in Belgian football.
"As a human being, he is an incredible character and a very intelligent man. I can't wait for him to join us and he's going to give us a real boost into the squad."