The Belgium international has one year remaining on his contract and has been the subject of constant speculation about an imminent move to the Bernabeu.
L’Equipe has reported that the La Liga giants will officially confirm the move after the final on May 29.
The 28-year-old’s sale will earn the Premier League club €100 million (around £86 million), according to the outlet.
An agreement was reached between the two clubs several weeks ago after the 28-year-old made it clear that he didn’t want to extend his contract at Stamford Bridge.
The move will see the winger team up with coach Zinedine Zidane, who returned to the Madrid bench in March after Santiago Solari's sacking.
Hazard explained after Chelsea’s final game of the Premier League season, a 0-0 draw with Leicester City, that his mind was already made up about his future.
“Yes. A couple of weeks ago. Yes I have made my decision but it is not just about me,” he said.
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