Arrizabalaga, 23, arrived at the club for a world record fee for a goalkeeper, 80 million euros (71.89 million pounds) from Spanish side Athletic Bilbao.
He replaces Thibaut Courtois, who joined Real Madrid this week.
“I know some players in the current team from the Spanish national side.
“All of them have told me what it’s like to play here and I have had excellent references from them about the game here,’’ Arrizabalaga told the club website.
Arrizabalaga has five compatriots in the Chelsea squad in Cesar Azpilicueta, Alvaro Morata, Marcos Alonso, Pedro and Cesc Fabregas.
“They’re all happy, comfortable at the club and encouraged me to make the move, have an international experience and it’s something I felt like doing,” the goalkeeper added.