The 30-year-old, who spent last season on loan at Bournemouth, joins the Gunners after the north London club activated his £5 million release clause.
Arrizabalaga signed for Chelsea in a deal worth €80 million (£71.6m) back in 2018, making him the world's most expensive goalkeeper.
In a statement released by Arsenal, he said: “I'm really, really happy to be here, really excited, and looking forward to what is coming.
“The ambition that is shown in this club, when I talk with Mikel (Arteta) and Inaki (Cana), how much they show me their desire to win, I think we are so close to winning and, hopefully, altogether, we can achieve it.”
Arrizabalaga started his career within the youth ranks of Athletic Bilbao, before joining Basconia, a feeder club for the top-flight outfit, in 2013.
The goalkeeper impressed and was fast-tracked into Athletic's reserves and then their first team by 2015.
Arrizabalaga left the Basque region for Chelsea in 2018, but he struggled to make an impact and was sent out on two loan deals.
The west London club sent him to Real Madrid for the 2023/24 season and to Bournemouth last term.