We present large-scale structure catalogs from the completed extended Baryon Oscillation Spectroscopic Survey (eBOSS). Derived from Sloan Digital Sky Survey (SDSS) -IV Data Release 16 (DR16), these catalogs provide the data samples, corrected for observational systematics, and random positions sampling the survey selection function. Combined, they allow large-scale clustering measurements suitable for testing cosmological models. We describe the methods used to create these catalogs for the eBOSS DR16 Luminous Red Galaxy (LRG) and Quasar samples. The quasar catalog contains 343,708 redshifts with $0.8 < z < 2.2$ over 4,808,deg$^2$. We combine 174,816 eBOSS LRG redshifts over 4,242,deg$^2$ in the redshift interval $0.6 < z < 1.0$ with SDSS-III BOSS LRGs in the same redshift range to produce a combined sample of 377,458 galaxy redshifts distributed over 9,493,deg$^2$. Improved algorithms for estimating redshifts allow that 98 per cent of LRG observations result in a successful redshift, with less than one per cent catastrophic failures ($Delta z > 1000$ ${rm km~s}^{-1}$). For quasars, these rates are 95 and 2 per cent (with $Delta z > 3000$ ${rm km~s}^{-1}$). We apply corrections for trends between the number densities of our samples and the properties of the imaging and spectroscopic data. For example, the quasar catalog obtains a $chi^2$/DoF$= 776/10$ for a null test against imaging depth before corrections and a $chi^2$/DoF$=6/8$ after. The catalogs, combined with careful consideration of the details of their construction found here-in, allow companion papers to present cosmological results with negligible impact from observational systematic uncertainties.
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