The deal for the 54-year-old contains a renewal provision until Euro 2024.
“I am coming again to a beautiful country with a rich history and nice people,” said the former Brighton and Sunderland coach.
Poyet replaces John van’t Schip who resigned the post last November.
Poyet is not new to Greece having coached AEK Athens to a third place finish in the Super League during the 2015-2016 season.
Poyet was capped 26 times by Uruguay and on a club level played for Chelsea, Spurs, Zaragoza, River Plate and Grenoble.