The length of deal matches the one that Kepa was on at San Mames, but the £195,000 weekly wages reported by the Daily Mirror represent a bumper pay rise and will see him earn around £70m if he stays for the full course of the contract.
It means that the 23-year-old will be paid just over £10m each season and will be one of highest earning goalkeepers in the world, a status that befits the most expensive in history.
Kepa's £71m move to Stamford Bridge has seen him overtake Alisson Becker in those stakes, with the Brazilian completing a £67m move from Roma to Liverpool last month.
Alisson broke the longstanding world record set when Gianlugi Buffon joined Juventus from Parma for the equivalent of €52m in the summer of 2001. His reign as the world's most expensive goalkeeper lasted 17 long years, but Alisson's was over after only 21 days.