The Italian takes over from Fernando Santos who left the country when his contract expired at the end of the World Cup.
Ranieri has signed a two-year contract which will take him up to the European Championships in France.
The Greeks lost on penalties to 10-man Costa Rica in a second-round of the World Cup after a match in which they missed several opportunities ended 1-1 in extra time.
However, they got a favourable reception when they returned to Athens after reaching the knockout stage for the first time in their history.
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- Sports & Recreation