We present the public release of the stellar mass catalogs for the GOODS-S and UDS fields obtained using some of the deepest near-IR images available, achieved as part of the Cosmic Assembly Near-infrared Deep Extragalactic Legacy Survey (CANDELS) project. We combine the effort from ten different teams, who computed the stellar masses using the same photometry and the same redshifts. Each team adopted their preferred fitting code, assumptions, priors, and parameter grid. The com- bination of results using the same underlying stellar isochrones reduces the systematics associated with the fitting code and other choices. Thanks to the availability of different estimates, we can test the effect of some specific parameters and assumptions on the stellar mass estimate. The choice of the stellar isochrone library turns out to have the largest effect on the galaxy stellar mass estimates, resulting in the largest distributions around the median value (with a semi interquartile range larger than 0.1 dex). On the other hand, for most galaxies, the stellar mass estimates are relatively in-sensitive to the different parameterizations of the star formation history. The inclusion of nebular emission in the model spectra does not have a significant impact for the majority of galaxies (less than a factor of 2 for _80% of the sample). Nevertheless, the stellar mass for the subsample of young galaxies (age < 100 Myr), especially in particular redshift ranges (e.g., 2.2 < z < 2.4, 3.2 < z < 3.6, and 5.5 < z < 6.5), can be seriously overestimated (by up to a factor of 10 for < 20 Myr sources) if nebular contribution is ignored.