They are now in the process of pushing that deal through after a protracted chase.
Hazard has never made any secret of his admiration for Madrid and dropped regular hints that he could one day head for Spain.
He is now getting that wish, with the 28-year-old moving to Santiago Bernabeu at the peak of his career.
Belgium international colleague Benteke is not surprised to see such a switch being made, with Hazard having always harboured the ambition of representing of the biggest clubs on the planet.
“Eden and I have known each other since we are young boys,” Benteke, who is currently on the books at Crystal Palace, told reporters.
“He always told me that Real Madrid is his dream club.
“His choice has therefore been made for a long time.
“I am happy for him that he is close to an agreement. I hope it will be fully official as soon as possible.”
For now, Hazard’s focus is locked on Euro 2020 qualification duty with his country.
Belgium are due to face Kazakhstan on Saturday, before then playing host to Scotland on Tuesday.
Once those games are out of the way, then Hazard will be free to make his way to Madrid.
He will be walking away from Chelsea after seven memorable years.
His time at Stamford Bridge has seen him make 352 appearances and score 110 goals.
Hazard is now a two-time winner of that competition, while his spell at Chelsea has also delivered two Premier League titles, FA Cup and League Cup triumphs and the 2014-15 PFA Player of the Year award.