The Asteroid Terrestrial-impact Last Alert System (ATLAS) carries out its primary planetary defense mission by surveying about 13000 deg^2^ at least four times per night. The resulting data set is useful for the discovery of variable stars to a magnitude limit fainter than r~18, with amplitudes down to 0.02 mag for bright objects. Here, we present a Data Release One catalog of variable stars based on analyzing the light curves of 142 million stars that were measured at least 100 times in the first two years of ATLAS operations. Using a Lomb-Scargle periodogram and other variability metrics, we identify 4.7 million candidate variables. Through the Space Telescope Science Institute, we publicly release light curves for all of them, together with a vector of 169 classification features for each star. We do this at the level of unconfirmed candidate variables in order to provide the community with a large set of homogeneously analyzed photometry and to avoid pre-judging which types of objects others may find most interesting. We use machine learning to classify the candidates into 15 different broad categories based on light-curve morphology. About 10% (427000 stars) pass extensive tests designed to screen out spurious variability detections: we label these as "probable" variables. Of these, 214000 receive specific classifications as eclipsing binaries, pulsating, Mira-type, or sinusoidal variables: these are the "classified" variables. New discoveries among the probable variables number 315000, while 141000 of the classified variables are new, including about 10400 pulsating variables, 2060 Mira stars, and 74700 eclipsing binaries.