We present the overall design and performance of the Astro-H (Hitomi) Soft X-Ray Spectrometer (SXS). The instrument uses a 36-pixel array of x-ray microcalorimeters at the focus of a grazing-incidence x-ray mirror Soft X-Ray Telescope (SXT) for high-resolution spectroscopy of celestial x-ray sources. The instrument was designed to achieve an energy resolution better than 7 eV over the 0.3-12 keV energy range and operate for more than 3 years in orbit. The actual energy resolution of the instrument is 4-5 eV as demonstrated during extensive ground testing prior to launch and in orbit. The measured mass flow rate of the liquid helium cryogen and initial fill level at launch predict a lifetime of more than 4 years assuming steady mechanical cooler performance. Cryogen-free operation was successfully demonstrated prior to launch. The successful operation of the SXS in orbit, including the first observations of the velocity structure of the Perseus cluster of galaxies, demonstrates the viability and power of this technology as a tool for astrophysics.