Transfer journalist Fabrizio Romano has revealed a deal has been done and Brighton will also get Chelsea's 19-year-old defender Levi Colwill as part of the transfer.
Personal terms for Cucurella were agreed on Monday, which has firmly shut the door on any approach Manchester City were planning on making, although the Premier League champions had been put off by the price-tag.
Cucurella is expected to undergo a medical in London on Thursday morning, and will also put the final touches to a six-year contract that will last until June 2028.
Once the deal is complete it will take Chelsea's spending on left-backs to nearly £100million in two years, as Ben Chilwell joined the club in August 2020 for £45million.
Chelsea, who have been looking for replacements for Marcos Alonso and Cesar Azpilicueta should they complete moves to Barcelona, have spotted an opportunity and have jumped in the market for the 24-year-old.
Cucurella moved from Getafe to Brighton in the summer of 2021 after the Seagulls splashed £15million on his signature.
The defender enjoyed an eye-catching start to his Premier League career and was even voted as the club's player of the season.
The Blues have already signed Raheem Sterling for £47million from Man City and Kalidou Koulibaly from Napoli for a further £33million.