Hazard has joined the La Liga giants from Chelsea after months of speculation.
Thousands of Los Blancos fans were at the Bernabeu to welcome the Belgian, who waved to the crowds.
Hazard is one of a number of signings by Real Madrid already this summer.
They have also secured Luka Jovic, Eder Militao, Ferland Mendy and Rodrygo.
But fans want another star signing with those at the Bernabeu chanting: “We want Mbappe.”
Paris Saint-Germain star Kylian Mbappe has been linked with a move to the Spanish capital.
Mbappe recently hinted he may move away from the Parc des Princes
“I want to thank all of the people who put together this league. I succeeded in adapting in my first year, to change position this year,” he said.
“There were some disappointments, but that is part of football. This is a very important moment for me.
“I am arriving at the second turning point in my career. I have discovered an enormous amount of things here.
“It is maybe the moment to have more responsibilities, maybe at PSG, with pleasure, or elsewhere for a new project.
“When you are in such an occasion you can send messages, I think I have sent mine.
“If I speak more it will be too much and that is not the message I wish to send.”
PSG boss Thomas Tuchel is keen to keep his stars though.
“My wish as a manager and as a coach is clear,” he said.
“I want all my players to stay at PSG and stay with our project. The work is not finished, it has just started.
“My wish is clear, but I can’t promise as that would be naïve and I don’t want to be naïve in this business.”
Hazard is unlikely to be fussed by the chanting at the Bernabeu, admitting the move is a dream.
“I will speak in French as my Spanish is not yet good enough,” he said.
“Thank you Mr President and thanks to my family.
“I want to win many titles with Real Madrid, in this shirt.
“This has been my dream since I was a child and now I’m here. I just want to enjoy this moment.
“I just want to enjoy this moment. Thank you very much.”