The 20-year-old finalised a late move on deadline day, having failed to start any of Chelsea's opening four games of the season
The Belgium international will now look to make his mark alongside fellow newcomers Gareth Barry and James McCarthy, who also completed last-gasp moves.
And Martinez is confident Lukaku, who scored 17 goals in 35 appearances at West Brom last season, will leave Everton fans with a smile this term.
"He's still a young man but he's got everything," he told the club's official website.
"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.
"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.
"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."
Another person who is enthused by the Belgium international's arrival is compatriot Kevin Mirallas, with the 25-year-old revealing he helped to give Lukaku a nudge towards a switch to Merseyside.
"I was with Romelu in his room at the team hotel on Monday night, and I only left when I was sure he was joining us," the winger added.
"I was surprised to learn we were in for him, because there had been no inkling, but once I got word, I really went to work.
"I just tried to convince him that Everton was the right step to take and he would love it at Goodison, and I’m really pleased he took it on board."
