Real ended their long pursuit of the winger on Friday when they agreed to sign him from Chelsea on a five-year contract for a reported 100 million euros (£89 million).
Hazard, who scored 110 goals in 352 games for Chelsea after joining from Lille in 2012, will be officially presented at the Santiago Bernabeu stadium next Thursday.
“He is an unbelievable personality. His focus in a match lies in the winning of the game," Martinez told reporters.
“He is now playing the best football of his career and he is a player around which a new project can be built,” added the Spaniard, whose side top Group I and looking for a fourth win out of four when they host the Scots in Brussels on Tuesday.
“Eden is a phenomenal footballer and I think for him several new chapters can be written about his career. The move to Real is his dream, the perfect next step.
“The whole transfer happened with a lot of respect. Eden is an example to all of a player who can go back to all his old clubs with his head held high.
Hazard, 28, is moving to Spain after helping Chelsea win the Europa League and finish third in the Premier League.
“I’m looking forward to seeing him at work at Real,” added Martinez who will be relying on his captain to help beat third-placed Scotland, who are three points behind the leaders.
“I’m not planning to change much,” he said of his team selection after Saturday’s 3-0 home win over Kazakhstan.
“We don’t underestimate any visitors. Scotland have got some real talent and coach Steve Clarke is one of the gentlemen of the game.”
Martinez was subjected at Monday’s new conference to a gentle ribbing about divided family loyalty since his wife, Beth, is Scottish.
“Well, we put a ban up at home so we aren't speaking about football since the Kazakhstan game, but I hope that everyone is very upset when I get home.
“She's no problem, it's more my father-in-law," joked Martinez.
(Reporting by Mark Gleeson in Cape Town; Editing by Ken Ferris)
