The 62-year-old Italian was out of work after parting company with Monaco, runners-up to Ligue 1 champions Paris Saint-Germain, in May.
He replaces Portugal's Fernando Santos who quit after taking Greece to the last 16 at the World Cup.
"I had other offers but once I met with the president of the federation I had a good feeling," former Chelsea boss Ranieri said.
He added: "I saw Greece at the World Cup and they gave me a very good impression and I loved their spirit. We will continue to work hard and look to produce the best results in Euro 2016."
Ranieri had led Monaco to Ligue 1 promotion in 2013, and still had one year left on his contract.
Aside from his time at Chelsea he also had spells with Serie A clubs Inter Milan, Napoli, Fiorentina, Juventus, Roma and Parma as well as Spanish outfits Atletico Madrid and Valencia.
"The Italian coach, with service in many major European clubs, is expected to lead our representative group to new successes in Euro 2016," the Greek federation announced.
Federation president Giorgos Sarris added: "It is an opportunity to take the national team to reach an even higher level. I thank him for accepting our proposal."
Local media reports suggested Ranieri has been given an annual salary of 800 000 euros, not including bonuses.