The Belgium international landed on Merseyside for a flying visit from his homeland on Wednesday to finalise a five-year contract after a £28million deal - believed to be a £25million fee with subsequent add-ons - was agreed with Chelsea.
Everton's previous record was the £15million paid to Standard Liege in 2006 for midfielder Marouane Fellaini, who moved on to Manchester United last summer for £28million.
Martinez stressed, however, the player will not carry that burden into the dressing room.
"Rom is vitally important but his transfer fee will not count for anything in terms of him developing and having an important role in the side," said the Spaniard
"This dressing room has got a special feeling and it is not about how much you pay for players to come in, it is about selecting the players to be in there.
"We really needed Rom at the club and that is where the chairman (Bill Kenwright) and the board have been exceptional, and I do think it is a key moment at our club.
"I am looking at that number nine position - and I am probably biased - but he is potentially the best choice in world football.
"In years to come you will see him develop into someone special, but nothing changes for Rom.
"He needs to enjoy his football, have the same standards he had and I am excited to see how far Rom can take us and how far we can take Rom.
"That is the partnership we can see here.
"It is true this moment in Rom's career is very significant because he is very ambitious, he wants to be successful and win things and wants to develop to the top of his potential.
"That is what we want to be as a team, so it is a perfect fit."
Lukaku said he is comfortable with the transfer fee and intends to provide the goals, having scored 16 in 33 appearances on loan at Goodison Park last season, to help fire the club into the Champions League.
Asked how long it could be until the Toffees were playing alongside Europe's elite, the Belgian said: "If we continue to develop like we did last season very soon.
"I wanted to stay in the Premier League because it is the most attractive league in the world and also the best.
"For me it was easy to stay here and help the team reach that level.
"I think the club wants to make a statement and I want to help the club to make a statement in this league.
"I don't put myself under pressure and just want to help my team-mates make this team as good as possible."
Martinez is still keen to add more signings, having already secured another loan player Gareth Barry on a permanent deal and also brought in £4million midfielder Muhamed Besic.
However, he may now have to rely on loan signings - the Toffees have been linked with a temporary deal for Chelsea's Christian Atsu - having used most of his transfer budget to secure Lukaku.
"I said before we signed Rom we need three attacking players and that has not changed," said the Everton boss.
"I always said money shouldn't be the difference between being able to challenge or not.
"It excites me when I see the side we have
Maybe some have the excuse of having to have a certain amount of money to challenge for titles, but I don't look at it that way."
Source : PA
Source: PA