Hazard joined Madrid from Premier League side Chelsea on a five-year deal last week for a fee that could reportedly rise to €140million.
The Belgium star will lead Zinedine Zidane's squad overhaul as the LaLiga giants look to bounce back from their third-place finish in 2018-19.
And Martinez believes Hazard and Madrid fit perfectly together as Belgium prepare for Tuesday's Euro 2020 qualifier against Scotland.
"For Real Madrid, they are getting a phenomenal footballer and for Eden, there couldn't have been too many new chapters in his career," Martinez said.
"He always said that he was feeling at home in London with Chelsea so probably it was the only place that he could have gone and the place where he always had the dream of going.
"I think it is the perfect fit. Everything has been commanded with incredible respect in every party and I think that's the way things should be done. Now we all look forward to seeing how his new chapter at Real Madrid will start."
Hazard – who led Chelsea to Europa League glory this season – is the fourth new arrival at Zidane's Madrid ahead of the 2019-20 campaign.
The 28-year-old follows Eder Militao, Luka Jovic and Rodrygo Goes to the Spanish capital club, with Madrid also reportedly eyeing Lyon full-back Ferland Mendy, Manchester United star Paul Pogba and Paris Saint-Germain's Neymar.