No single person invented colors, as they are naturally occurring. However, the person who formulated the concept of viewing objects, and parts of objects, as having different shades and hues was Sir Isaac Newton.
Peterman's Eye claims that Sir Isaac Newton made an attempt at explaining the idea of color during the early 1660's, when he was only "Isaac Newton." Newton's discovery of color is related to the refraction of light from his light/prism experiments. This ultimately gave the human race knowledge about how the eyes "perceive" colors depending on the way they reflect and refract surrounding light, allowing every person to see colors differently.