The west London club completed a world-record deal for the 23-year-old last night and he will train with his new team-mates today.
However, speculation over that transfer has cooled in recent weeks and it appears the 27-year-old will begin his seventh season with Chelsea when their Premier League campaign starts at Huddersfield Town this weekend.
"It's an accumulation of things, and I am very glad Chelsea has chose to trust me and to take me in as well".
Courtois signed for Chelsea from Genk in the summer of 2011 and immediately went on loan to Atletico Madrid, where he won a La Liga title, the Europa League and the Copa del Rey as well as reaching a Champions League final in three seasons working under Diego Simeone.
Despite that impressive signing, Maurizio Sarri's main acquisition before the deadline is set to be Kepa.
He told Chelsea's official website.
"He has already demonstrated fantastic quality and consistency and will be a big part of any success Chelsea have in the coming years", Chelsea director Marina Granovskaia said.
With Thibaut Courtois seemingly on his way out of Stamford Bridge ahead of his move to Spanish giants Real Madrid, Chelsea have taken their first steps towards securing his replacement.
Earlier on Wednesday, Bilbao confirmed that Kepa had paid his buyout clause at the league´s headquarters in Madrid to free him from his contract with Athletic.
Belgian star Courtois will sign a six-year contract at the Santiago Bernabeu, however, Navas has no plans to leave Madrid.
He has spent the past two seasons in Bilbao's first team, making 53 La Liga appearances, and has one global cap.
Kepa made his worldwide debut for Spain in November, keeping a clean sheet in a friendly win over Costa Rica, and was named to the Spain squad for the World Cup in Russian Federation this summer, though he didn't play.