We present the final Sloan Digital Sky Survey IV (SDSS-IV) quasar catalog from Data Release 16 of the extended Baryon Oscillation Spectroscopic Survey (eBOSS). This catalog comprises the largest selection of spectroscopically confirmed quasars to date. The full catalog includes two subcatalogs (the current versions are DR16Q_v4 and DR16Q_Superset_v3 at https://data.sdss.org/sas/dr16/eboss/qso/DR16Q/): a "superset" of all SDSS-IV/eBOSS objects targeted as quasars containing 1,440,615 observations and a quasar-only catalog containing 750,414 quasars, including 225,082 new quasars appearing in an SDSS data release for the first time, as well as known quasars from SDSS-I/II/III. We present automated identification and redshift information for these quasars alongside data from visual inspections for 320,161 spectra. The quasar-only catalog is estimated to be 99.8% complete with 0.3%-1.3% contamination. Automated and visual inspection redshifts are supplemented by redshifts derived via principal component analysis and emission lines. We include emission-line redshifts for Hα, Hβ, Mg II, C III], C IV, and Lyα. Identification and key characteristics generated by automated algorithms are presented for 99,856 broad absorption-line quasars and 35,686 damped Lyman alpha quasars. In addition to SDSS photometric data, we also present multiwavelength data for quasars from the Galaxy Evolution Explorer, UKIDSS, the Wide-field Infrared Survey Explorer, FIRST, ROSAT/2RXS, XMM-Newton, and Gaia. Calibrated digital optical spectra for these quasars can be obtained from the SDSS Science Archive Server.