The first eROSITA all-sky survey (eRASS1) performed onboard of the Spectrum-Roentgen-Gamma mission (SRG) provides more than 900000 X-ray sources in the 0.2-2.3keV band located in the western hemisphere. We present identifications of the eRASS1 sources obtained using our HamStar method, which was designed for the identification of coronal X-ray sources. HamStar is a Bayesian framework that estimates coronal probabilities for each eRASS1 source based on a cross-match with optical counterparts from Gaia DR3. It considers geometric properties, such as the angular separation and positional uncertainty, as well as additional properties namely the fractional X-ray flux, color, and distance. We identify 138800 coronal eRASS1 sources and estimate a completeness and reliability of about 91.5% for this sample, which we confirmed with Chandra detections. This is the largest available sample of coronal X-ray emitters and we find nearly five times as many coronal sources as in the ROSAT all-sky survey. The coronal eRASS1 sources are made up sources of all spectral types and the onset of convection and the saturation limit are clearly visible. As opposed to previous samples, rare source types are also well populated. About 10% of the coronal eRASS1 sources have a correlated secondary counterpart, which is a wide binary companion or belongs to the same stellar cluster. We also identify 6700 known unresolved binaries, and an excess of fast binary periods below 10d. Furthermore, the binary sequence is clearly visible in a color-magnitude diagram. When combining the coronal eRASS1 sources with rotation modulations from Gaia DR3, we find 3700 X-ray sources with known rotation periods, which is the largest sample of this kind. We fitted the rotation-activity relation and convection turnover times for our flux limited sample. We do not detect the low-amplitude fast rotators discovered in the Gaia DR3 sample in X-rays.