The "Aetos Dios" (Ancient Greek: άετός Διός) is translated from Greek into "Eagle of Zeus". There are two schools of thought regarding the origin of this eagle, coming from different Greek legends. The eagle was once a mortal king named Periphas.
According to Antoninus Liberalis, Periphas was a legendary king of Attica who was a just king, and a dutiful priest of Apollo. Zeus however became indignant because Periphas was revered and honoured as if he were Zeus himself, so Zeus wanted to destroy Periphas and his entire household. But Apollo interceded, and instead Zeus transformed Periphas into an eagle, making him king of all birds and guard of his sacred sceptre.
In other accounts the eagle was in fact an ancient creation of the goddess Gaia. He appeared before Zeus at the start of the Titanomachy (Battle of the Titans). Zeus took this to mean a good omen of victory, leading to him using the emblem of a golden eagle on his war standard:
"...For so happy an omen, especially since victory did ensue, he made a golden eagle for his war standards and consecrated it to the might of his protection, whereby also among the Romans, standards of this kind are carried." — a translated excerpt from Fulgentius' "Mythologies" (Mythologiarum Libri III)