We identify multi-wavelength counterparts to 1147 submillimeter sources from the S2COSMOS SCUBA-2 survey of the COSMOS field by employing a recently developed radio+machine-learning method trained on a large sample of Atacama Large Millimeter/submillimeter Array (ALMA)-identified submillimeter galaxies (SMGs), including 260 SMGs identified in the AS2COSMOS pilot survey. In total, we identify 1222 optical/near-infrared (NIR)/radio counterparts to the 897 S2COSMOS submillimeter sources with S_850_>1.6mJy, yielding an overall identification rate of (78+/-9)%. We find that (22+/-5)% of S2COSMOS sources have multiple identified counterparts. We estimate that roughly 27% of these multiple counterparts within the same SCUBA-2 error circles very likely arise from physically associated galaxies rather than line-of-sight projections by chance. The photometric redshift of our radio+machine-learning-identified SMGs ranges from z=0.2 to 5.7 and peaks at z=2.3+/-0.1. The AGN fraction of our sample is (19+/-4)%, which is consistent with that of ALMA SMGs in the literature. Comparing with radio/NIR-detected field galaxy population in the COSMOS field, our radio+machine-learning-identified counterparts of SMGs have the highest star formation rates and stellar masses. These characteristics suggest that our identified counterparts of S2COSMOS sources are a representative sample of SMGs at z<~3. We employ our machine-learning technique to the whole COSMOS field and identified 6877 potential SMGs, most of which are expected to have submillimeter emission fainter than the confusion limit of our S2COSMOS surveys (S_850um_<~1.5mJy). We study the clustering properties of SMGs based on this statistically large sample, finding that they reside in high-mass dark matter halos ((1.2+/-0.3)x10^13^h^-1^M_{sun}_), which suggests that SMGs may be the progenitors of massive ellipticals we see in the local universe.