Hazard joined Madrid from Premier League side Chelsea on a five-year deal on Friday for a fee that could reportedly rise to €140m (£124m/$146m) with incentives.
The Belgium international attacker won two Premier League titles and as many Europa League crowns during his time at Chelsea, where he played alongside Courtois before the star goalkeeper left for Madrid in 2018-19.
And Courtois – whose first season in Madrid resulted in a third-place finish in La Liga – is expecting big things from Hazard at the Santiago Bernabeu.
"If he speaks a little Spanish, it will be even better," Courtois said following Belgium's 3-0 Euro 2020 qualifying win over Kazakhstan on Saturday.
"It's very nice that we're going to be together. He's my friend, I get along very well with him and his family.
"For Madrid it's going to be fantastic. I think [Hazard] is going to make the difference and I hope we can win many titles next season."
But the goalkeeper was not the only Belgium team-mate happy for the winger for making the move to the Spanish giants.
Napoli forward Dries Mertens also praised Hazard following his move to Madrid, calling it a "good step forward" for the 28-year-old.
"I'm happy for him, it's a good step forward," Mertens, who scored against Kazakhstan, said post-match. "He's already one of the best players in the world, and now he has to take advantage of his opportunities to become the best of all."
Hazard – who led Chelsea to Europa League glory this season – is the fourth new arrival at Zinedine Zidane's Madrid ahead of the 2019-20 campaign.
He 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.