We report the discovery of a transiting brown dwarf companion to KOI-205, a K0 main-sequence star, in a 11.720125-day period orbit. The transits were detected by the Kepler space telescope, and the reflex motion of the star was measured using radial velocity observations obtained with the SOPHIE spectrograph. The atmospheric parameters of the host stars were determined from the analysis of high-resolution, high signal-to-noise ratio ESPaDOns spectra obtained for this purpose. Together with spectrophotometric measurements recovered from the literature, these spectra indicate that the star is a mildly metallic K0 dwarf with T eff 5237 ± 60 K. The mass of the companion is 39.9 ± 1.0 M Jup and its radius is 0.81 ± 0.02 R Jup , in agreement with current theoretical predictions. This is the first time a bona fide brown dwarf companion is detected in orbit around a star of this type. The formation and orbital evolution of brown dwarf companions is briefly discussed in the light of this new discovery.