The Blues entered the race for the Spaniard earlier this month after Manchester City ended the pursuit of his services
City were reluctant to pay more than £40 million, and Chelsea have since managed to seal the deal for the defender.
According to Fabrizio Romano , the Blues have paid an initial £55m for Cucurella with a further £7m in add-ons.
He has now become the Blues' fifth summer purchase after Raheem Sterling , Kalidou Koulibaly , Gabriel Slonina and Carney Chukwuemeka .
The west London giants are expected to spend further with claims that they are strongly interested in two more players.
Barcelona's Frenkie de Jong and Leicester City 's Wesley Fofana have been heavily tipped to join the club this month.
The Blues are in advanced negotiations for Fofana, but will need to pay at least £85m to convince the Foxes to do business.