It is widely known that color names across the world's languages tend to be organized into a neat hierarchy with a small set of "basic names" featuring in a comparatively fixed order across linguistic societies. However, to date, the basic names have only been defined through a set of linguistic principles. There is no statistical definition that quantitatively separates the basic names from the rest of the color words across languages. Here we present a rigorous statistical analysis of the World Color Survey database hosting color word information from 110 non-industrialized languages. The central result is that those names for which a population of individuals show a larger overall agreement across languages turn out to be the basic ones exactly reproducing the color name hierarchy and, thereby, providing, for the first time, an empirical definition of the basic color names.