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We report the discovery of TOI-2119b, a transiting brown dwarf (BD) that orbits and is completely eclipsed by an active M-dwarf star. Using light curve data from the Transiting Exoplanet Survey Satellite mission and follow-up high-resolution Doppler spectroscopic observations, we find the BD has a radius of $R_b = 1.08 \pm 0.03{\rm R_J}$, a mass of $M_b = 64.4 \pm 2.3{\rm M_J}$, an orbital period of $P = 7.200865 \pm 0.00002$ days, and an eccentricity of $e=0.337\pm 0.002$. The host star has a mass of $M_\star = 0.53 \pm 0.02{\rm M_\odot}$, a radius of $R_\star= 0.50 \pm 0.01{\rm R_\odot}$, an effective temperature of $T_{\rm eff} = 3621 \pm 48$K, and a metallicity of $\rm [Fe/H]=+0.06\pm 0.08$. TOI-2119b joins an emerging population of transiting BDs around M-dwarf host stars, with TOI-2119 being the ninth such system. These M-dwarf--brown dwarf systems typically occupy mass ratios near $q = M_b/M_\star \approx 0.1-0.2$, which separates them from the typical mass ratios for systems with transiting substellar objects and giant exoplanets that orbit more massive stars. The nature of the secondary eclipse of the BD by the star enables us to estimate the effective temperature of the substellar object to be $2030\pm 84$K, which is consistent with predictions by substellar evolutionary models.