The player's representatives and lawyers travelled to La Liga headquarters in Valencia to pay the fee, with Kepa now due to travel to London to undergo a medical and finalize personal terms, goal.com reported.
Athletic confirmed that the release clause had been paid on Wednesday, issuing a statement that read, "The player Kepa Arrizabalaga has met the requirements for the valid unilateral termination of the contract that linked him to Athletic Club.
"Athletic thanks the player for his contribution during the time he has remained with our club."
The Kepa deal will break the club's previous transfer record, set last season when the Blues signed Alvaro Morata from Real Madrid in an initial £58m ($75m) deal, potentially rising to £70m ($90m).
It will also make Kepa the world's most expensive goalkeeper, less than a month after Alisson joined Liverpool in a £65m (€73m/$85m) move.
The move for the Spaniard will free up Thibaut Courtois to complete a switch to Real Madrid, with the Belgian having been absent from training as he looked to force through a switch to Santiago Bernabeu.
Madrid has been keen to bring in Courtois in a €35m deal (£31m/$40m) for some time now, where the funds expected from that transfer being used by the Blues to secure Athletic goalkeeper Kepa.
And the Blues' transfer business isn't likely to end with Kepa –goal.com understands Maurizio Sarri's side is in talks over a loan move for Madrid midfielder Mateo Kovacic.
Indeed, Madrid boss Julen Lopetegui has revealed that his side will attempt to find a "high level replacement" should Kovacic complete a switch to Stamford Bridge.
Time is against Sarri and Chelsea, however, with the transfer window for Premier League clubs closing at 5pm BST today.
Chelsea gets its Premier League campaign underway on Saturday with an away trip to David Wagner's Huddersfield Town.