The deal for the Spain left-back is said to be worth £51.8 million in total, broken down as a fixed £47.5 million fee and £4.3 million in add-ons.
Cucurella joined Chelsea in 2022 and made 163 appearances for the Blues.
The 27-year-old endured a rocky start in West London, but established himself as a starter under the guidance of Enzo Maresca.
Cucurella won the Conference League and Club World Cup during the spell, both in 2025.
Cucurella is currently at the World Cup with Spain, who kick off their campaign against Cape Verde on Monday.
He currently has 23 caps for his country and was part of the side that won Euro 2024.