We present the Data Release 10 Quasar (DR10Q) catalog from the Baryon Oscillation Spectroscopic Survey (BOSS) of the Sloan Digital Sky Survey III. The catalog includes all BOSS objects that were targeted as quasar candidates during the first 2.5 years of the survey and that are confirmed as quasars via visual inspection of the spectra, have luminosities Mi[z = 2] <-20.5 (in a ΛCDM cosmology with H0 = 70 km s-1 Mpc-1, ΩM = 0.3, and ΩΛ = 0.7), and either display at least one emission line with a full width at half maximum (FWHM) larger than 500 km s-1 or, if not, have interesting/complex absorption features. The catalog also includes known quasars (mostly from SDSS-I and II) that were reobserved by BOSS. The catalog contains 166 583 quasars (74 454 are new discoveries since SDSS-DR9) detected over 6373 deg2 with robust identification and redshift measured by a combination of principal component eigenspectra. The number of quasars with z > 2.15 (117 668) is ~5 times greater than the number of z > 2.15 quasars known prior to BOSS. Redshifts and FWHMs are provided for the strongest emission lines (C iv, C iii, Mg ii). The catalog identifies 16 461 broad absorption line quasars and gives their characteristics. For each object, the catalog presents five-band (u, g, r, i, z) CCD-based photometry with typical accuracy of 0.03 mag and information on the optical morphology and selection method. The catalog also contains X-ray, ultraviolet, near-infrared, and radio emission properties of the quasars, when available, from other large-area surveys. The calibrated digital spectra cover the wavelength region 3600-10 500 Å at a spectral resolution in the range 1300 < R < 2500; the spectra can be retrieved from the SDSS Catalog Archive Server. We also provide a supplemental list of an additional 2376 quasars that have been identified among the galaxy targets of the SDSS-III/BOSS. Quasar catalog is only available at the CDS via anonymous ftp to http://cdsarc.u-strasbg.fr (ftp://130.79.128.5) or via http://cdsarc.u-strasbg.fr/viz-bin/qcat?J/A+A/563/A54