The club announced the £71.6m signing of Kepa from Athletic Bilbao just hours after confirming the departure of Thibaut Courtois to Real Madrid and loan arrival of midfielder Mateo Kovacic in the opposite direction.
He joins on a season-long loan ahead of the new season.
The Belgium worldwide, named best goalkeeper at the World Cup this summer, has signed a six-year deal after completing a medical on Thursday.
Courtois said at his official unveiling: "Arriving at the best club in the world is a responsibility and an honour".
Explaining the reasons for his move, the Golden Glove victor at World Cup 2018 said: "I wanted to be closer to my family".More news: Does this mean Kourtney Kardashian and Younes Bendjima have split?
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His future has always been speculated amid Madrid's pursuit of Manchester United keeper David de Gea, however, the veteran has played a key role in the capital. Everything, all the titles the club has won, all the players at the club, the city, the English Premier League.
The 23-year-old has signed a seven-year deal at Stamford Bridge, where he will take over between the sticks from Belgium's Thibaut Courtois.
Kepa had been with Athletic since 2004, rising through the youth ranks.
The fee is a world record for a goalkeeper, surpassing the £65m paid by Liverpool to Roma for Brazil goalkeeper Alisson Becker last month.
While not discussing the status of the transfer, Chelsea coach Maurizio Sarri said that Kepa was "very young, but very, very good".