The 28-year-old is set to step in for Thibaut Courtois, who sustained a torn anterior cruciate ligament (ACL) in his left knee during a training session last Thursday, leading to several months of absence.
Kepa was acquired by Chelsea from Athletic Bilbao in 2018 for a club record of 80 million euros.
However, he fell out of favour with the London club, which recently acquired goalkeeper Robert Sanchez from Brighton & Hove Albion.
Although Bayern Munich reportedly pursued Kepa, aiming to replace their injured goalkeeper Manuel Neuer, Real Madrid acted swiftly to secure the deal.
Courtois’ injury poses a significant setback for Real Madrid, as they will be without a key player for the foreseeable future.
The goalkeeper is likely to make his debut later this week against Almeria as Real Madrid seek their second win of the season.