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We present large-scale structure catalogs from the completed extended BaryonOscillation 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 thesurvey selection function. Combined, they allow large-scale clusteringmeasurements suitable for testing cosmological models. We describe the methodsused to create these catalogs for the eBOSS DR16 Luminous Red Galaxy (LRG) andQuasar 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 over4,242\,deg$^2$ in the redshift interval $0.6 < z < 1.0$ with SDSS-III BOSS LRGsin the same redshift range to produce a combined sample of 377,458 galaxyredshifts distributed over 9,493\,deg$^2$. Improved algorithms for estimatingredshifts allow that 98 per cent of LRG observations result in a successfulredshift, 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 betweenthe number densities of our samples and the properties of the imaging andspectroscopic 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 ofthe details of their construction found here-in, allow companion papers topresent cosmological results with negligible impact from observationalsystematic uncertainties.

The Completed SDSS-IV extended Baryon Oscillation Spectroscopic Survey: Large-scale Structure Catalogs for Cosmological Analysis