PSG host relegation battling Le Havre on Saturday
The 62-year-old Ranieri takes over from Fernando Santos who left the role when his contract expired after this year's World Cup
He will lead Greece into their qualifying campaign for the 2016 European Championship in France.
One of the most experienced coaches in European club football, Ranieri has managed Fiorentina, Valencia, Atletico Madrid, Chelsea, Parma, Juventus, Roma, Inter Milan and Monaco.
Greece lost on penalties to 10-man Costa Rica in the World Cup second round in Brazil last month.