The clubs did not disclose financial terms, but British media reported the deal was worth up to 51.8 million pounds ($69.5 million).
"Real Madrid and Chelsea FC have reached an agreement for the transfer of the player Marc Cucurella, who will be linked to our club for the next six seasons, until June 30, 2032," Real said in a statement.
Real are looking to strengthen after a disappointing 2025-26 season, in which they missed out on the LaLiga title and were eliminated from the Champions League in the quarter-finals.
Club president Florentino Perez, who recently extended his reign by four more years, had promised to bolster Real's defensive options during his re-election campaign.
Cucurella joined Chelsea from Brighton & Hove Albion in 2022 for a reported deal worth up to 63 million pounds, and went on to make 163 appearances in all competitions for the west London club.
The 27-year-old endured a rocky first season at Stamford Bridge, struggling for form and consistency.
He later established himself as a regular under manager Enzo Maresca, often deployed as an inverted full-back, and won the Conference League and the Club World Cup in 2025.
He has also become a key part of the Spanish national team since making his debut for them in 2021, earning 23 caps for Luis de la Fuente's side and winning the European Championship in 2024. He is in the country's squad for the 2026 World Cup.
In March, Cucurella publicly criticised Chelsea's youth-heavy recruitment strategy, saying the club needed to strike a better balance between youth and experience.
Chelsea finished the 2025-26 Premier League season in 10th place, outside European qualification places.