Even though astrology/astronomy started in the Near East (Sumer, Babylon, Egypt) the signs of the zodiac as we use them today find their complete explanation in the context of Greek mythology. An excellent website brings a few versions of the same basic story. Here's the story that appears in the 1st century C.E. book titled Catasterismi (Greek: placing among the stars), which is a collection of ancient Hellenistic sources. In The Astronomy Fragment 4 there, which was translated by Evelyn-White, Greek poet Hesiod (from the 8th century B.C.E.) is quoted as saying that:
Orion went away to Crete and spent his time hunting in company with Artemis and Leto. It seems that he threatened to kill every beast, there was on earth; whereupon, in her anger, Ge (the Earth) sent up against him a Scorpion of very great size by which he was stung and so perished. After this Zeus, at the prayer of Artemis and Leto, put him among the stars, because of his manliness, and the Scorpion also as a memorial of him and of what had occurred.
Other sources add that this story about the enmity between Scorpion and Orion explains why they are never seen in the sky at the same time: one of them sets as the other rises.