He is expected to sign a five-year contract.
With a £72m price-tag said to have been "triggered", the deal would smash the £67m paid by rivals Liverpool for former Blues target Alisson last month, while also well beating the record-price paid by Chelsea for a player - that was last summer when Alvaro Morata arrived for £58m.
The deal that sees Courtois join Real Madrid for a reported £35million sees midfielder Mateo Kovacic head the other way on a season-long loan.
In total he has played 141 official games with the club, and won three Champions Leagues, one League, four Club World Cups, three European Super Cups and one Spanish Super Cup.
"Courtois doesn't come to Chelsea training", noted Catalan daily Mundo Deportivo, for whom "his destination will be Real Madrid".
"It's an accumulation of things, and I am very glad Chelsea has chose to trust me and to take me in as well".
"On Wednesday August 8th 2018, at 12:02 p.m., the Professional Football League has certified to our entity that the player Kepa Arrizabalaga has fulfilled the requirements for the valid unilateral termination of the employment contract that linked him to Athletic Club", read a statement on Bilbao's website.
Chelsea announce that Thibaut Courtois will leave the club, while Mateo Kovacic joins on loan.
"The cited note points out that the player has stated his wish to end and resolve unilaterally his contractual relationship that had started in the 2004/05 campaign and has deposited the compensation fee that was established in his contract".
Spanish radio station Onda Cero claimed Madrid hope to unveil Courtois at Santiago Bernabeu on Thursday, with personal terms for a deal already agreed.
There is also speculation that Chelsea could try to sign Atletico Madrid's Jan Oblak.
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