It is a saga that has been running for more than two seasons now, but according to L'Equipe, the move will be made official in the aftermath of the Blues' all-English Europa League final with Arsenal.
Rumours of the transfer's completion have been swirling around for weeks, with the fee understood to be the final stumbling block in the negotiations. Recent reports had claimed that, despite Hazard's contract expiry date of June 2020, Los Blancos were willing to break their club record transfer fee of €100m - shelled out for Gareth Bale back in 2013 - to sign the Belgian.
However, it is now understood that this figure will not be breached, with the famed French publication reporting that the fee will come 'close to €100m' but not exceed it. And the official unveiling will now occur in the days following the final in Baku on 29 May, with Hazard eager to end his Stamford Bridge tenure on a high, and not have the club's build-up to the final disrupted.
As has been mooted for some time - and indeed as Hazard essentially revealed to the press following Sunday's Premier League clash against Leicester - this deal has been in place for at least a few weeks now.
Indeed, after Barcelona's 3-0 first leg triumph against Liverpool in the Champions League semi-final looked to have confirmed Barça's place in the final, Madrid were readying their presentation of the forward for 2 June, in an attempt to provide hope to supporters should their rivals have won the competition the evening prior.
Any Chelsea fans clinging onto the hope that their talismanic Belgian will be staying put were dealt a near-fatal blow on Sunday, when the player explained: "I have made my decision but it is not just about me. I told the club a couple of weeks ago. I wanted it to be cleared up earlier but that's not happened. I'm still waiting, like the fans are waiting.
"We have a final to play and then I will see. It has never been a distraction. When you are on the pitch, you try to be focused on the pitch with the ball. That's it. When I am on the pitch I just try to do the best. I am not thinking about this and this, my situation or the club's situation. I just try to win games." [Credit:90mins]