According to BBC Sport, the Blues have chose to part ways with Courtois this summer following weeks of speculation regarding his future.
Madrid confirmed Courtois will undergo his medical on Thursday before being unveiled to the club's fans at the Bernabeu.
"Kepa is a talent we have admired for a long time and we are extremely excited about his arrival", insisted Chelsea director Marina Granovskaia.
The deal brings an end to a protracted saga which culminated in Courtois declining to report for Chelsea training on Monday in an attempt to force the club to sell him, having informed Maurizio Sarri last week that he wanted to leave.
Goalkeeper Thibaut Courtois is off to Real Madrid from Chelsea. But it is likely to be around £35m, as reported earlier.
Courtois played for Atletico between 2011-2014 on loan from Chelsea before moving back to Stamford Bridge and becoming first choice there, forcing legend Petr Cech out of the squad.
Athletic said the 23-year-old Kepa had his €80-million (NZ$138m) buyout clause paid on Wednesday, although the Spanish club did not say which team made the payment. Not necessarily. Especially when you consider Chelsea's Premier League rivals Liverpool beating the Blues to a perhaps more tested Allison.
- Everything you need to know about the Saudi Arabia-Canada fallout
- Indonesian rescuers struggle to reach cut-off villages after deadly quake
- Karunanidhi, Indian political icon, dies at 94
- At least 20 dead in strikes on Yemen's Hodeida - medics
- Facebook removes Alex Jones, Infowars pages for hate, bullying
- Moms of 11 children found at filthy New Mexico compound arrested
- Venezuelan leader Maduro accuses Colombia of exploding drone assassination attempt
- Ernesto Valverde to decide Yerry Mina Barcelona future Jordi Mestre
- Manafort trial day 4: Accountant concedes possible wrongdoing, Manafort's double life
- Manchester City's message for rivals is clear: be afraid