The 42-year-old, who has previously managed Anzhi Makhachkala, Sivasspor and Akhisar Belediyespor, replaces Harm van Veldhoven at the club.
Delhi finished fifth in the standings last term, with the new season kicking off in October.
"I want to inform you that I am the new coach of Delhi dynamos in India," Carlos posted on his Instagram page.
"It is an interesting project of a growing club! I'm very happy to be part of this club!"
Meanwhile, Carlos's ex-Real teammate Nicolas Anelka was named Mumbai City's player-manager on Friday.