Kepa, who joined Athletic at the age of 10, was part of the Spain squad that lost to Germany in the final of the Under-21 European Championship in 2017 and was also part of the senior group at the 2018 World Cup, alongside David De Gea and Pepe Reina.
Upon completing his move to Chelsea, he said: 'It's a very important decision for me, for my career, and also for my personal life.
Chelsea tried to sign Jan Oblak, who has a £90 million release clause, but the goalkeeper wanted to stay at Atletico Madrid.
He has played 53 times in La Liga for Bilbao over the last two seasons, and made his global debut in a 5-0 friendly win over Costa Rica in November 2017.
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Arrizabalaga, who only signed a new seven-year deal with Athletic in January, becomes Maurizio Sarri's second high profile signing since taking charge, following in the footsteps of midfielder Jorginho, who followed Sarri from Napoli for around £50m.
Chelsea open their Premier League campaign at Huddersfield on Saturday, having suffered a 2-0 defeat to Manchester City in the Community Shield last weekend.
But it is not just Kepa's transfer fee that will raise eyebrows, as Chelsea have agreed to pay the 23-year-old roughly £10m-a-year over seven years - taking the total value of the transfer to £141.6m. After playing for Inter Milan and Real Madrid, Kovačić's stint at Chelsea will make him the fifth Croatian footballer in history to wear the jersey of the London club.
Real Madrid will now likely get on with their bid to get Thibaut Courtois into the club, with the Belgian missing the first two days of training deliberately in a bid to force through a move back to Madrid where his family are based.