Hazard joined La Liga giants Madrid from Chelsea on a five-year deal on Friday for a fee of €100 million (£88m/$112m), but with incentives could rise to as much as €140m (£124m/$146m).
It put to end months of speculation surrounding Hazard, who had professed his desire to join Real Madrid as early as last summer but enjoyed another strong season for the Blues under Maurizio Sarri.
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.
Courtois, who forced Chelsea's hand by refusing to sign a new contract last summer, had encouraged Hazard to follow his lead and join Madrid on multiple occasions during the season.
And now that his Belgium international team-mate has officially done so, Courtois welcomed Hazard to the Santiago Bernabeu via social media as the pair prepare to reunite in Madrid.
"Welcome to the best club in the world!!! @hazardeden10 @realmadrid," Courtois wrote on Twitter.
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.
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.
The Liga giants are looking to return to their old heights next season, after struggling in 2018-19, with the Club World Cup trophy their only haul for the season.
The club finished third in the league this season, 19 points behind champions Barcelona and eight behind local rivals Atletico, while they saw their string of three straight Champions League titles come to an end when they were knocked out by Ajax in the last 16.
Madrid sacked Zidane's initial successor, Julen Lopetegui at the end of October, and replacement Santiago Solari in March, with the France legend returning to the fold.
Courtois started 27 games in La Liga this season, while managing eight clean sheets for the club in the league.