Kepa, 23, arrives at Stamford Bridge after a release clause in his contract was met, with the deal surpassing Alisson’s £66.8m move to Liverpool.
He has signed a seven-year contract at the club and replaces Thibaut Courtois, who is set to join Real Madrid.
Kepa is second choice for Spain behind Manchester United’s David de Gea.
He has spent the past two seasons in Athletic’s first team, making 53 La Liga appearances, and has one international cap.
The fee Chelsea have paid surpasses the £60m they spent on Spanish striker Alvaro Morata in July 2017.
“So many things attracted me to the club – all the titles the club has won, the other players, the city, the English Premier League,” Kepa said.
“It’s an accumulation of things, and I am very glad Chelsea has decided to trust me and to take me in as well.”
In January, Kepa signed a new long-term contract with Athletic until 2025, amid interest from Real Madrid.
He is the second key player to leave the club this year, after Manchester City signed French defender Aymeric Laporte for £57m in January.
“Kepa is a very solid goalkeeper, who can become an even better goalkeeper in the years to come,” European football writer Andy Brassell told BBC Radio 5 live. “He was deemed good enough by the board and (former manager) Zinedine Zidane to be good enough for Real Madrid, but they wouldn’t pay the clause.”
A world record – for 20 days
Before Alisson moved from Roma to Liverpool in July, Gianluigi Buffon had spent 17 years as the most expensive goalkeeper in world football.
The 40-year-old Italian, who this summer left Juventus to join Paris St-Germain, was purchased for 53m euros by Juve from Parma on 3 July 2001.
While that record stood for 6,225 days, the fee paid for Alisson was surpassed within 20 days.