© 2016. The American Astronomical Society. All rights reserved.We cross-match the two currently largest all-sky photometric catalogs - mid-infrared Wide-field Infrared Survey Explorer and SuperCOSMOS scans of UKST/POSS-II photographic plates - to obtain a new galaxy sample that covers 3p steradians. In order to characterize and purify the extragalactic data set, we use external GAMA and Sloan Digital Sky Survey spectroscopic information to define quasar and star loci in multicolor space, aiding the removal of contamination from our extended source catalog. After appropriate data cleaning, we obtain a deep wide-angle galaxy sample that is approximately 95% pure and 90% complete at high Galactic latitudes. The catalog contains close to 20 million galaxies over almost 70% of the sky, outside the Zone of Avoidance and other confused regions, with a mean surface density of more than 650 sources per square degree. Using multiwavelength information from two optical and two mid-IR photometric bands, we derive photometric redshifts for all the galaxies in the catalog, using the ANNz framework trained on the final GAMA-II spectroscopic data. Our sample has a median redshift of zmed = 0.2, with a broad dN/dz reaching up to z > 0.4. The photometric redshifts have a mean bias of |dz|, ~ 10-3 a normalized scatter of s z = 0.033, and less than 3% outliers beyond 3s z. Comparison with external data sets shows no significant variation of photo-z quality with sky position. Together with the overall statistics, we also provide a more detailed analysis of photometric redshift accuracy as a function of magnitudes and colors. The final catalog is appropriate for "all-sky" three-dimensional (3D) cosmology to unprecedented depths, in particular through cross-correlations with other large-area surveys. It should also be useful for source preselection and identification in forthcoming surveys, such as TAIPAN or WALLABY.