Arrizabalaga will arrive as a temporary replacement for Thibaut Courtois, who will be sidelined for several months after suffering a torn anterior cruciate ligament (ACL) in his left knee during a training session last Thursday.
Arrizabalaga joined Chelsea from Athletic Bilbao in 2018 for a record 80 million euros fee for a goalkeeper but fell out of favour in the London club, who signed goalkeeper Robert Sanchez from Brighton & Hove Albion this summer.
He has reportedly been targeted by Bayern Munich as the German side are seeking to replace their own injured goalkeeper, Manuel Neuer, but Real Madrid moved faster to secure the deal.
Courtois' injury is a major blow for Real as they will have to make do without the services of one of their key players for the foreseeable future.
Courtois joined Real from Chelsea in 2018 after winning two Premier League titles, the FA Cup and the League Cup during his time at Stamford Bridge.
He was named Player-of-the-Match following the 2022 Champions League final after producing one of the greatest goalkeeping performances in a European Cup final.
Courtois recorded nine saves to deny Liverpool in Paris, leading his club to a record-extending 14th European title after a 1-0 win.
Real Madrid had only one other goalkeeper in their first-team squad, Ukraine's Andriy Lunin.
The 24-year-old Lunin has made only nine Spanish league appearances for the club since signing from Zorya Luhansk in 2018. He spent his first two seasons in Spain on loan spells with Leganes, Valladolid and Oviedo.
