The Sloan Digital Sky Survey (SDSS) has been in operation since 2000 April. This paper presents the Tenth Public Data Release (DR10) from its current incarnation, SDSS-III. This data release includes the first spectroscopic data from the Apache Point Observatory Galaxy Evolution Experiment (APOGEE), along with spectroscopic data from the Baryon Oscillation Spectroscopic Survey (BOSS) taken through 2012 July. The APOGEE instrument is a near-infrared R similar to 22,500 300 fiber spectrograph covering 1.514-1.696 mu m. The APOGEE survey is studying the chemical abundances and radial velocities of roughly 100,000 red giant star candidates in the bulge, bar, disk, and halo of the Milky Way. DR10 includes 178,397 spectra of 57,454 stars, each typically observed three or more times, from APOGEE. Derived quantities from these spectra (radial velocities, effective temperatures, surface gravities, and metallicities) are also included. DR10 also roughly doubles the number of BOSS spectra over those included in the Ninth Data Release. DR10 includes a total of 1,507,954 BOSS spectra comprising 927,844 galaxy spectra, 182,009 quasar spectra, and 159,327 stellar spectra selected over 6373.2 deg(-2).