We study the composition of the faint radio population selected from the Karl G. Jansky Very Large Array Cosmic Evolution Survey (VLA-COSMOS) 3 GHz Large Project, which is a radio continuum survey performed at 10 cm wavelength. The survey covers a 2.6 square degree area with a mean rms of ∼2.3 µJy/beam, cataloging 10 830 sources above 5σ, and enclosing the full 2 square degree COSMOS field. By combining these radio data with optical, near-infrared (UltraVISTA), and mid-infrared (Spitzer/IRAC) data, as well as X-ray data (Chandra), we find counterparts to radio sources for ∼93% of the total radio sample reaching out to z 6; these sources are found in the unmasked areas of the COSMOS field, i.e., those not affected by saturated or bright sources in the optical to near-infrared (NIR) bands. We further classify the sources as star-forming galaxies or AGN based on various criteria, such as X-ray luminosity; observed mid-infrared color; UV-far-infrared spectral energy distribution; rest-frame, near-UV optical color that is corrected for dust extinction; and radio excess relative to that expected from the star formation rate of the hosts. We separate the AGN into subsamples dominated by low-to-moderate and moderate-to-high radiative luminosity AGN, i.e., candidates for highredshift analogs to local low-and high-excitation emission line AGN, respectively. We study the fractional contributions of these subpopulations down to radio flux levels of ∼11 µJy at 3 GHz (or ∼20 µJy at 1.4 GHz assuming a spectral index of -0.7). We find that the dominant fraction at 1.4 GHz flux densities above ∼200 µJy is constituted of low-to-moderate radiative luminosity AGN. Below densities of ∼100 µJy the fraction of star-forming galaxies increases to ∼60%, followed by the moderate-to-high radiative luminosity AGN (∼20%) and low-to-moderate radiative luminosity AGN (∼20%). Based on this observational evidence, we extrapolate the fractions down to sensitivities of the Square Kilometer Array (SKA). Our estimates suggest that at the faint flux limits to be reached by the (Wide, Deep, and UltraDeep) SKA1 surveys, a selection based only on radio flux limits can provide a simple tool to efficiently identify samples highly (>75%) dominated by star-forming galaxies.