Real Madrid are believed to be the front-runners to sign the shot-stopper this summer, as some of the goalkeeper's family are already living in the Spanish capital.
In return, Julen Lopetegui's side has sanctioned a one-season loan spell at Chelsea for midfielder Kovacic, who is yet to fully settle at the Santiago Bernabeu.
On social media, the World Cup Golden Glove victor has faced the wrath of furious Chelsea supporters.
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Kepa is second choice for Spain behind Manchester United's David de Gea. "I want to win many titles here".
Kepa is eligible to make his debut for Chelsea in the Premier League opener against Huddersfield Town on Saturday and said: "It's a very important decision for me, for my career, and also for my personal life".
With just a year remaining on his contract, the 26-year-old had been absent from training this week as he looked to push through a move before the transfer window ended for Chelsea on Thursday. Considered Spain's goalkeeper of the future, he was a reserve at the World Cup in Russian Federation.
Chelsea, of course, had to break the record fee for a goalkeeper, set by Alisson Becker a few weeks back, when they paid £71.5 million for Kepa.