The 70-year-old has signed a one-year contract to replace Claudio Ranieri, who was sacked in November following an embarrassing defeat against the Faroe Islands.
Makarian – a former Peru and Paraguay coach – is charged with the task of turning Greece's fortunes around when their qualifying campaign recommences in March.
"The allocation of responsibility to be coach of the national team, for me is a great honour," said the Uruguayan.
"I want to thank the Federation, who chose me for this position.
"We have a difficult task ahead of us, but I believe in my work, as well as the Greek footballers."
Greece are bottom of Group F with just one point from four games and Ranieri paid the price when he was relieved of his duties after just four months in charge.
They travel to Budapest on March 29, before the return fixture with the Faroe Islands in June.
