According to BBC Sport, the Blues have made a decision to part ways with Courtois this summer following weeks of speculation regarding his future.
"Kepa is a talent we have admired for a long time and we're extremely excited about his arrival", she intimated to Chelsea's official website.
Real Madrid said Courtois will sign a six-year contract at the Santiago Bernabeu, where he will face competition from incumbent Keylor Navas for the No. 1 spot.
Kepa could make his Premier League debut against Huddersfield on Saturday after completing a deal that director Marina Granovskaia believes will be great for Chelsea.More news: Trevor Noah: Why Paul Manafort Must Be So Proud
One of the main storylines of this summer's transfer window was would happen with the future of Belgian goalkeeper Thibaut Courtois and what Chelsea would do at the goalkeeper position.
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.
Stamford Bridge has also agreed terms for the permanent transfer of Thibaut Courtois to Real Madrid. But it is likely to be around £35m, as reported earlier.
Kepa, 23, joins from Athletic Bilbao after Chelsea paid his release clause to bring him to the Premier League.
Courtois has been on strike this week in an effort to force Chelsea to sell him, and the team relented after lining up Kepa Arrizabalaga as his replacement. The midfielder will join Jorginho in Chelsea's midfield who joined the Blues from Napoli.