The 23-year-old has put pen to paper on a seven-year deal at the Blues and will be the club's No 1 following the departure of Thibaut Courtois.
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.
He has played 53 times in La Liga for Bilbao over the last two seasons, and made his worldwide debut in a 5-0 friendly win over Costa Rica in November 2017.
After being strongly linked to Real Madrid, Arrizabalaga signed a new deal with Bilbao in January which raised his release fee to 80 million from 20 million.
His future has always been speculated amid Madrid's pursuit of Manchester United keeper David de Gea, however, the veteran has played a key role in the capital.
Kepa told the club's website "It's a very important decision for me, for my career, and also for my personal life". So, I don't know.
He will train with his new Chelsea teammates for the first time on Thursday and could even make his debut in the club's opening Premier League fixture against Huddersfield Town on Saturday.
The Golden Glove victor will then undergo medicals on Thursday and will be presented as a Real Madrid player at 1:00 PM local time.