The Belgium star, who spent three seasons at Atletico Madrid from 2011 to 2014, wanted to move closer to his two children in the Spanish capital and had stayed away from training with Chelsea this week in a bid to force through the transfer.
Real, meanwhile, confirmed Courtois will undergo a medical on Thursday morning before signing a six-year deal.
Chelsea completed the club-record signing of Kepa Arrizabalaga on Wednesday, hours after Athletic Bilbao confirmed the trigger of his €80 million (£71.5m) release clause, making him the world's most expensive goalkeeper.
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.
Kepa is Spain's number two behind Manchester United'sDavid de Gea. Considered Spain's goalkeeper of the future, he was a reserve at the World Cup in Russian Federation.
The statement made no mention of Chelsea, but the move represents a world record for a goalkeeper, surpassing the £65m paid by Liverpool to Roma for Brazil goalkeeper Alisson Becker last month.
It's no secret that Kovacic is extremely unhappy at Real Madrid, so much so that he refused to train with the first team upon his return to the club. The Croatian midfielder competed with regular Madrid starters Casemiro, Toni Kroos and Luka Modric.