Ultra-deep radio surveys are an invaluable probe of dust-obscured star formation, but require a clear understanding of the relative contribution from radio active galactic nuclei (AGNs) to be used to their fullest potential. We study the composition of the Jy radio population detected in the Karl G. Jansky Very Large Array COSMOS-XS survey based on a sample of 1540 sources detected at 3 GHz over an area of ∼350 arcmin2. This ultra-deep survey consists of a single pointing in the well-studied COSMOS field at both 3 and 10 GHz and reaches rms sensitivities of 0.53 and 0.41 Jy beam−1, respectively. We find multiwavelength counterparts for 97% of radio sources, based on a combination of near-UV/optical to sub-millimeter data, and through a stacking analysis at optical/near-IR wavelengths we further show that the sources lacking such counterparts are likely to be high-redshift in nature (typical z ∼ 4−5). Utilizing the multiwavelength data over COSMOS, we identify AGNs through a variety of diagnostics and find these to make up 23.2 1.3% of our sample, with the remainder constituting uncontaminated star-forming galaxies. However, more than half of the AGNs exhibit radio emission consistent with originating from star formation, with only 8.8 0.8% of radio sources showing a clear excess in radio luminosity. At flux densities of ∼30 Jy at 3 GHz, the fraction of star formation-powered sources reaches ∼90%, and this fraction is consistent with unity at even lower flux densities. Overall, our findings imply that ultra-deep radio surveys such as COSMOS-XS constitute a highly effective means of obtaining clean samples of star formation-powered radio sources.