Athletic confirmed on Wednesday that the 23-year-old's release clause of 80million euros (£71m) was activated and his contract terminated, although made no mention of Chelsea.
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.
Sources told ESPN FC that Kepa boarded a flight from Bilbao Airport on Tuesday, with Spanish newspaper AS reporting that he is set to meet with his representatives in Madrid and decide whether to make the move to Stamford Bridge.
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Arrizabalaga, who only signed a new seven-year deal with Athletic in January, becomes Maurizio Sarri's second high profile signing since taking charge, following in the footsteps of midfielder Jorginho, who followed Sarri from Napoli for around £50m. I am very happy here.
"Chelsea and Real Madrid have tonight agreed terms for the permanent transfer of Thibaut Courtois subject to the agreement of personal terms and passing a medical", Chelsea signalled in a statement published on the club's official website.
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"Those who are close to me or more know me know that I am a person who likes to analyse everything before making a decision".
Courtois' intentions were concrete - Real Madrid are the only he side he wishes to play for, and to prepare for life without him Chelsea have deemed Kepa to be the only suitable replacement.
Real, meanwhile, confirmed Courtois will undergo a medical on Thursday morning before signing a six-year deal.
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As the part of the contract, Mateo Kovacic, midfielder of the Spanish powerhouse, will join the blues on a season-long loan. Transfer fee for the Belgian's move has not been disclosed by the clubs.