A statement on Athletic's website read: "Kepa Arrizabalaga has met the requirements for the valid unilateral termination of the work contract that linked him to Athletic Club".
The west London club completed a world-record deal for the 23-year-old last night and he will train with his new team-mates today.
Courtois, part of the Belgium team that enjoyed their most successful ever World Cup, was due to return to training on Monday, but didn't show up.
"Athletic thanks the player for his contribution during the time he has remained in our club".
Courtois spent three years on loan at Atlético Madrid from Chelsea, before becoming Chelsea's No 1 in 2014-15.
Athletic do not negotiate when it comes to selling their top stars because they limit themselves to only signing Basque players, meaning the only way Chelsea could bring Kepa to Stamford Bridge was by activating his buyout clause.More news: PUBG launches 'Fix PUBG' website
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If Chelsea's 2-0 loss to Manchester City in the Community Shield was anything to go by, the idea of reserve goalkeeper Willy Caballero playing week-in, week-out wouldn't be much comfort to supporters - and the arrival of Robert Green doesn't do much to reassure, either.
Courtois played a total of 154 appearances for Chelsea, winning the Premier League on two occasions.
Kepa is eligible to make his debut for Chelsea in the Premier League opener against Huddersfield Town on Saturday and said: "It's a very important decision for me, for my career, and also for my personal life".
Real, meanwhile, confirmed Courtois will undergo a medical on Thursday morning before signing a six-year deal. Transfer fee for the Belgian's move has not been disclosed by the clubs.
He will move to Stamford Bridge as a replacement for Belgium global Thibaut Courtois, who earlier this evening sealed his long anticipated move to European Champions Real Madrid.