The Hubble Catalog of Variables (HCV) is the first full, homogeneous, catalog of variable sources found in the Hubble Source Catalog (HSC), which is built out of publicly available images obtained with the WFPC2, ACS and WFC3 instruments onboard the Hubble Space Telescope. The HCV is the deepest catalog of variables available. It includes variable stars in our Galaxy and nearby galaxies, as well as transients and variable active galactic nuclei. The HCV contains 84,428 candidate variable sources (out of 3.7 million HSC sources that were searched for variability) with V <= 27 mag; for 11,115 of them the variability is detected in more than one filter. The number of data points in a light curve range from 5 to 120, the time baseline ranges from under a day to over 15 years, while ~8% of variables have amplitudes in excess of 1 mag. Two catalogs are provided in this HLSP: a catalog of variables, and a catalog of objects that are 'constant' within 5-sigma of their median absolute deviation (MAD). The catalog of variables lists for each source the equatorial coordinates, MatchID, GroupID, subgroup, the pipeline classification flag, the expert-validation classification flag, the number of existing instrument and filter combinations for the source, the name of the instrument and filter combination. The filter combination includes: the filter detection flag (set to '1' if variability is detected, or '0' if not), the variability quality flag, the number of measurements in the light curve, the HSC magnitude, the corrected magnitude, the MAD value, and the reduced chi^2 value. For all multi-filter variable candidates, there are extra columns for each additional instrument and filter combination, in which the source is classified as a variable candidate. The catalog of constant sources contains the sources that fall below the 5-sigma detection threshold of the HCV pipeline. These include constant sources and low-amplitude variables that are below the detection threshold. For each source, the columns show the equatorial coordinates, the MatchID, the GroupID, the subgroup, the number of instrument and filter combinations in which individual sources are observed, follwed by the name of each instrument and filter combination for which the following data are given: the number of measurements in the light curve, the HSC magnitude, the corrected magnitude, the MAD value, and the reduced chi^2 value.