With Thibaut Courtois joining Real Madrid, Chelsea signed 23-year-old Arrizabalaga as an instant replacement for the Belgium international.
Arrizabalaga becomes the most expensive goalkeeper in football history, ahead of Liverpool's Alisson, who moved from AS Roma for 75 million euros earlier in the transfer window.
"The Spanish international goalkeeper arrives ahead of the new Premier League season having signed a seven-year contract at Stamford Bridge," Chelsea said in a statement.
Athletic confirmed earlier on Wednesday that Arrizabalaga's representatives deposited his buy-out clause at La Liga's offices.
"He has already demonstrated fantastic quality and consistency and will be a big part of any success Chelsea have in the coming years," Chelsea director Marina Granovskaia said.
"His long-term contract reflects the belief we have in him and we look ahead to the coming seasons with an enormous sense of optimism."
Arrizabalaga has played 53 La Liga matches for Athletic Bilbao since breaking into the team in 2016.
"It's a very important decision for me, for my career, and also for my personal life," said the goalkeeper.
"So many things attracted me to the club, all the titles the club has won, the other players, the city, the English Premier League.
"It's an accumulation of things, and I am very glad Chelsea has decided to trust me and to take me in as well."
After being strongly linked to Real Madrid, Arrizabalaga signed a new deal with Bilbao in January which raised his release fee to 80 million from 20 million.
Chelsea coach Maurizio Sarri praised Arrizabalaga on Tuesday night.
"I saw (Kepa) one year ago, my first impression was that he is a very good goalkeeper, very young but very good," said the Italian coach after his team drew 0-0 with Olympique Lyonnais in a friendly.
(Reporting by Rik Sharma, Editing by Ed Osmond)
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