The two clubs are believed to have agreed a deal worth £88million initially.
It could rise another £42m due to add-ons with Hazard set to be unveiled at the Bernabeu at the end of next week.
The move has been in the pipeline since last summer and with Hazard out of contract next summer, Chelsea were keen to cash in.
Though it’s not just the Blues who will feel the benefits in their pocket with Hazard set to too.
The Evening Standard report that Hazard will see his salary increase from £200,000 to £400,000 at Real Madrid.
It’s claimed that it took the Belgian just a few hours to accept the offer with Hazard handed a five-year deal.
He will become one of the best-paid players at Real Madrid on completion of the move.
Hazard is currently with the Belgium national team and his unveiling will not be until the end of the internationals.
And Hazard’s compatriot Christian Benteke has revealed his move to Real Madrid has always been a wish.
“Eden and I have known each other since we are young boys,” Benteke said.
“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.”
Hazard had admitted he was likely to leave Chelsea following the Blues’ Europa League victory over Arsenal.
“I think it’s a goodbye,” he said. “But in football you never know.
“My dream was to play in the Premier League. I think it’s time for a new challenge.
“I’ve made my decision. Now it depends on the clubs. Both clubs.”