Real Madrid announced in its statement Courtois will sign a six-year contract, and the club will present him to its fans Thursday at Santiago Bernabeu Stadium.
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.
Kepa may be a relatively unknown name for Chelsea fans and Premier League watchers, but there's a reason that Real Madrid were so eager to move for him just a few months ago.
Courtois played a total of 154 appearances for Chelsea, winning the Premier League on two occasions.
'It's a very important decision for me, for my career, and also for my personal life, ' he said. Mario Stanić was the first, followed by goalkeeper Matej Delač, striker Stipe Perica, and offensive midfielder Marijo Pašalić, though they have all been sent out on loan from The Blues.More news: Explosion kills chief of Syrian chemical weapons plant
"Athletic thank the player for his contribution throughout the time he has been at the club".
In January, Madrid were set to meet his then-release clause of €20m as it looked increasingly unlikely that Navas would be renewing his contract with Madrid.
The 23-year-old has signed a seven-year contract with the English giants.
Tottenham defender Toby Alderweireld has been eyeing a move away from the north London club and could be a target for United, who appear to have missed out on Bayern Munich's Jerome Boateng.
As part of the deal taking Courtois to Madrid, Croatian midfielder Matteo Kovacic will join Chelsea on a season-long loan deal from Real.
Chelsea's transfer window has suddenly gone from bad to slightly better as the Blues have finally completed a huge swap deal with Real Madrid.