Hazard is Real's top transfer target as the Spanish club rebuild after a dismal season and the Belgium star appears set to complete his move to the Bernabeu in the next few days.
A Daily Telegraph report said Real and Chelsea came to an agreement over the terms of the deal on Thursday after several days of negotiations.
Real had originally offered around £88 million, but it is claimed the final fee could rise as high as £130 million when all the bonus payments are included.
The basic fee for Hazard is expected to reach £100 million, the sum for which Chelsea had been holding out despite the 28-year-old entering the final year of his Stamford Bridge contract.
Hazard is on the verge of leaving Chelsea after seven years, having won two Premier League titles, two Europa League crowns, one FA Cup and one League Cup.
He scored twice in Chelsea's 4-1 Europa League final win over Arsenal in Baku last month, then immediately admitted he expected his time at Stamford Bridge to come to an end.
Hazard has been hoping for a move to Real for over a year, with Chelsea blocking his attempt to leave last year before the Blues finally accepted his wish in the closing weeks of the season.
Speaking after the Europa League final, Hazard had said: "I think it's a goodbye. My dream was to play in the Premier League, I did it for seven years. Maybe it's time for a new challenge."
