The AllWISE Source Catalog contains astrometry and photometry for 747,634,026 objects detected on the deep AllWISE Atlas Intensity Images. Positions, magnitudes, astrometric and photometric uncertainties, flags indicating the reliability and quality of the source characterizations, and associations with the 2MASS Point and Extended Source Catalog sources are presented for each source. New to the AllWISE Source Catalog are measurements of the apparent motion of each source that exploit the two independent WISE sky coverage epochs. The AllWISE Source Catalog is superior to the WISE All-Sky Release Catalog and should be your primary reference for discrete objects in the mid-IR sky, with the one exception described below. The AllWISE Catalog sensitivity is better in the W1 and W2 bands because of increased depth-of-coverage provided by the coaddition of data from the 4-Band, 3-Band and Post-Cryo survey phases. The photometric accuracy in all four bands is improved because faint source flux biases have been corrected and background estimation has been made more robust. Astrometry accuracy is better because of the correction for the proper motion of 2MASS astrometric reference stars in the 11 years between the two surveys, and the incorporation of the multiple independent source measurements in the image overlap regions into the astrometric solutions. Measurements of the apparent motion of sources are provided for the first time, and improved source flux variability metrics have been computed. The WISE All-Sky Source Catalog provides better photometry for sources brighter than the saturation limit in bands W1 and W2, W1<8 mag and W2<7 mag, that were observed during the Post-Cryo survey phase. Saturated source photometry during the Post-Cryo phase is systematically biased with the respect to that in the other phases, when they were combined in for AllWISE the resulting measurements have larger net uncertainties. The All-Sky Catalog that is limited to data from the 4-Band Cryo phase does not suffer from this bias.