The 62-year-old Italian takes over from Fernando Santos after his contract expired following the World Cup, where he guided Greece to the last 16.
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 federation's website.
Transfers
Real Madrid reignite interest in Sterling despite dip in form - Paper Round
6 HOURS AGO
"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."
Premier League
Sheffield United relegated from Premier League after Wolves defeat
6 HOURS AGO
Copa del Rey
Messi hits brace as Barca blitz Athletic to lift Copa del Rey
9 HOURS AGO