No one really knows for sure when the constellations were first recognized but the Greeks are who came up with the modern constellation system. Astronomers can theorize about who first came up with the ideas of constellations due a phenomenon called precession. Precession has to do with the Earth's axis and the positioning of the celestial poles. Because of this information it seems that the constellations may have been originated by the Sumerians and Babylonians. This is of course just a theory.

Many of the constellations were given Greek names. They were replaced later in Latin.

The stars have been studied since the beginning of man. "The earliest known efforts to catalog the stars dates back to cuneiform texts and artifacts from 6000 years ago."  Most of our current constellations we can attribute to Roman, Greek, and Babylonian mythology.  Around the 7th century B.C., in the time of Homer, the stars were thought to replicate animals.  By the 5th century B.C. most of the constellations began to be associated with myths.  Mythology, of course, influenced the naming of many objects in the night sky, not just the constellations.  Planets and moons bear names from mythology.