Goal can confirm the two clubs have come to a compromise on Hazard's price following face-to-face talks between Chelsea director Marina Granovskaia and Real Madrid CEO Jose Angel Sánchez in London on Monday, allowing the 28-year-old to make what he has described as a "dream" move.
Hazard is set for a significant pay-rise upon joining Madrid after turning down multiple contract offers from the west London club, and he could be formally unveiled at Santiago Bernabeu next week after he returns from international duty with Belgium.
The former Lille wideman will also get the opportunity to play under manager Zinedine Zidane, whom he idolised as a player growing up, and he joins fellow summer signings Luka Jovic and Eder Militao in agreeing moves to the Blancos following their underwhelming 2018-19 campaign.
The defending European champions burned through three managers during the course of the season and finished with just the Club World Cup crown after losing out to Barcelona in both La Liga and Copa del Rey and an embarrassing Champions League exit at the hands of Ajax.
Hazard, meanwhile, has brought the curtain down on a glorious eight years with Chelsea in which he won six major trophies, including the Europa League this season.
He scored twice in the 4-1 final victory over Arsenal in Baku, taking his final tally to 110 goals in 352 matches for the Blues.
He will become their record sale after 12 months of negotiations regarding his future.
Madrid showed their intent to sign Hazard last summer but a deal could not be reached despite the attacker hinting during Belgium's run to the World Cup semi-finals that he would be open to a move.
He instead entered the penultimate year of his contract at Stamford Bridge, and with no new deal ever looking likely to be agreed, Chelsea were put in a position in which they needed to sell their superstar before he left on a free transfer in the summer of 2020.
Chelsea rejected Madrid's opening offer for the player in April, but have finally come to an agreement, with Hazard set to reunite with international team-mate Thibaut Courtois, who made the same move last summer. Courtois will likely be forced act as a translator for his compatriot, who will enter a dressing room where few players speak either English or French.
The Blues have already signed Christian Pulisic from Borussia Dortmund in a bid to replace Hazard while fellow winger Callum Hudson-Odoi is set to bring an end to the debate regarding his future by signing a five-year deal with his boyhood club.
Chelsea, though, have their hands tied when it comes to bringing in any futher reinforcements during the summer transfer window, with their FIFA-imposed transfer ban set to come into play during the off-season.
An appeal to the Court of Arbitration for Sport (CAS) could see the ban delayed or even overturned, but for now there will be no new faces coming through the door.