This catalog combines Gaia DR1, Pan-STARRS 1, SDSS and 2MASS astrometry to compute proper motions for 350 million sources across three-fourths of the sky down to a magnitude of mr≈20. Positions of galaxies from Pan-STARRS 1 are used to build a reference frame for PS1, SDSS, and 2MASS data. Gaia DR1 is adapted to that reference frame by exploiting that locally, proper motions are linear. GPS1 has a characteristic systematic error of less than 0.3 mas/yr, and a typical precision of 1.5−2.0 mas/yr. The proper motions have been validated using galaxies, open clusters, distant giant stars and QSOs. In comparison with other published faint proper motion catalogs, GPS1's systematic error (<0.3 mas/yr) is about 10 times better than that of PPMXL and UCAC4 (>2.0 mas/yr). Similarly, its precision (~1.5 mas/yr) is an improvement by ∼ 4 times relative to PPMXL and UCAC4 (∼6.0 mas/yr). For QSOs, the precision of GPS1 is found to be worse (∼2.0−3.0 mas/yr), possibly due to their particular differential chromatic refraction (DCR).