In 330 the Emperor Constantine the Great changed the capital of the Roman Empire from Rome to Constantinople.
Greek population was part of the Empire and the Eastern part of the Roman Empire was already heavily Hellenized and Emperor Heraclius completed the Hellenization (replaced Latin with Greek as the official language, etc.)
He also, adopted the Greek title of Basileus instead of the Latin Caesar, Augustus, or Imperator.
Holdouts included Rhodes, conquered in 1522, Cyprus in 1571, Crete, retained by the Venetians until 1669, and the Ionian islands which remained primarily under the rule of the Republic of Venice.
Some trainers of the Hellenic Air Force who are training Afghanese pilots stayed there longer than the ELDAF-TESAF.