The 28-year-old Belgian will leave Stamford Bridge after seven hugely successful years at the club, winning the Premier League twice, one FA Cup and two Europa League titles.
This comes after negotiations between the clubs took place this week before a breakthrough was reached over the fee with the contract now ready to be signed.
According to Standard, Real Madrid will pay an initial fee of £88m but there are a number of add-ons included in the transfer which could see the Blues net another £42m.
Hazard, who is regarded as one of the best players in the world and has only 12 months left on his contract, scored 110 goals for the Blues and made 81 assists.
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