Ptolemy was Greek. He wrote an important book called the Almagest. In it, he lists and describes the constellations as used in Greece in the 4th century BC. Naturally, the Greeks used elements from Greek Mythology in their sky culture, just as Chinese sky culture uses elements from Chinese legend and myth.
Ptolemy's Almagest and Greek sky culture influenced the Hellenistic world, and through Rome, it influenced the whole of Western Europe. Then through European expansion, it came to influence the whole world.
There are several additions to Ptolemy's system: The Southern Sky was divided into constellations by Europeans in the 15th century, and there are several additions to the Northern sky, such as Coma Berencies (Hair of Berenice II of Egypt) and Camelopardalis, the giraffe, (added in the 15th century)