Caballero, 35, joins as a backup to Belgian Thibaut Courtois. Chelsea allowed former no.2 Asmir Begovic to join Bournemouth earlier this summer.
The Argentine told his new club's official website: "I am very happy to join Chelsea, the champions of England.
"I am looking forward to meeting the guys and helping the club achieve more success in the coming season."
He is the Champions' first signing of the season.