We present the selection algorithm and anticipated results for the Time Domain Spectroscopic Survey (TDSS). TDSS is an Sloan Digital Sky Survey (SDSS)-IV Extended Baryon Oscillation Spectroscopic Survey (eBOSS) subproject that will provide initial identification spectra of approximately 220,000 luminosity-variable objects (variable stars and active galactic nuclei across 7500 deg2 selected from a combination of SDSS and multi-epoch Pan-STARRS1 photometry. TDSS will be the largest spectroscopic survey to explicitly target variable objects, avoiding pre-selection on the basis of colors or detailed modeling of specific variability characteristics. Kernel Density Estimate analysis of our target population performed on SDSS Stripe 82 data suggests our target sample will be 95% pure (meaning 95% of objects we select have genuine luminosity variability of a few magnitudes or more). Our final spectroscopic sample will contain roughly 135,000 quasars and 85,000 stellar variables, approximately 4000 of which will be RR Lyrae stars which may be used as outer Milky Way probes. The variability-selected quasar population has a smoother redshift distribution than a color-selected sample, and variability measurements similar to those we develop here may be used to make more uniform quasar samples in large surveys. The stellar variable targets are distributed fairly uniformly across color space, indicating that TDSS will obtain spectra for a wide variety of stellar variables including pulsating variables, stars with significant chromospheric activity, cataclysmic variables, and eclipsing binaries. TDSS will serve as a pathfinder mission to identify and characterize the multitude of variable objects that will be detected photometrically in even larger variability surveys such as Large Synoptic Survey Telescope.