Ranieri has been handed a two-year deal and his main focus will now be steering Greece to Euro 2016.
"Claudio Ranieri signed a two-year contract with the Greek Football Federation and is the new coach of the national team," read a statement on the Greek football federation’s website.
"The Italian coach, with service at many major European clubs, is expected to lead our group to new successes with Euro 2016 on the horizon."
Ranieri’s first match in charge will be a European Championship qualifier against Romania on September 7 with Northern Ireland, Hungary, Finland and the Faroe Islands also providing the competition in Group F.
The experienced tactician has been out of work since his sacking by Monaco in May after two seasons in the principality.
Ranieri made his name in his native Italy winning the Coppa Italia with Fiorentina before moving to Valencia where he won the Copa del Rey and the Intertoto Cup.
Four seasons at Chelsea followed before a brief return to Valencia and spells at Parma, Juventus, Roma and Inter Milan.