The 62-year-old had signed a two-year deal to take charge of the team and succeeds Fernando Santos, who stepped down after guiding Greece to the last 16 of this summer's World Cup, where they were eliminated on penalties to Costa Rica.
Ranieri guided newly promoted Ligue 1 club Monaco to second place last season but was ruthlessly dismissed and, as such, was on the lookout for a new position and had been heavily linked with the Greece job for weeks.
"Claudio Ranieri signed a two-year contract with Greece and is the new coach of the national team," a statement from the HFF read on its website.
"The Italian coach, who has experience with many major European clubs, is expected to lead our group to new successes at EURO 2016."
The tenure will be the former Chelsea, Valencia and Juventus boss' first spell in charge of an international team during a managerial career that has spanned 28 years.
Ranieri will be expected to get Greece off to a good start in the team’s first Euro 2016 qualifying fixture against Romania at the Karaiskaki Stadium on September 7.
Greece, who famously won the tournament as major underdogs 10 years ago, will also have to face Hungary, Finland, Northern Ireland and Faroe Islands in Group F.