Babylonian astrology was very primitive. A strong magical system of correspondences was developed, linking heaven and earth; it was this magical world view that was taken over by the Greeks and mathematically developed into Aristotle's cosmology and what we know today as astrology. The Babylonians were practical people, interested in learning from their omens the tides of war and the coming of the floods so necessary for their agriculture. The Greeks were trying to build up a mathematical picture of the cosmos as a whole and for that reason are considered the forerunners of science.
But Greek astrology was not a science. Astrology came to the Greeks as a full-blown magical system, its assumptions and operating principles unquestioned. The Greeks wove astrology into their "scientific" cosmology, setting the pattern for astrologers to attach their "art" onto each new up-and-coming science, more and more ascribing astrology to physical influences and obscuring the magical principles upon which it was based.
Thus, Greek astrology used the same magical "principle of correspondences," adding the characteristics of their native gods to the planets and stars. Astrologers have long claimed that the characteristic influences of the stars were determined through patient observation over many centuries. This is totally false; the astrological nature of the signs and planets is determined strictly on the basis of their magical correspondences. Thus, Pisces (the Fish) is called a water sign, red Mars is associated with war, quick and elusive Mercury governs the metal quicksilver (mercury), planets in opposition are in disharmony, and so on.
It was the Egyptians who contributed planetary aspects (system of Places): the idea that planets at particular angles (opposition, square, trine) represent omens foretelling events on earth. The Greeks merely superimposed the Egyptian system of Places on the Babylonian zodiac (way of Anu) to come up with what we know today as astrology.