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We report the discovery of a transiting brown dwarf companion to KOI-205, aK0 main-sequence star, in a 11.720125-day period orbit. The transits weredetected by the Kepler space telescope, and the reflex motion of the star wasmeasured using radial velocity observations obtained with the SOPHIEspectrograph. The atmospheric parameters of the host stars were determined fromthe analysis of high-resolution, high signal-to-noise ratio ESPaDOns spectraobtained for this purpose. Together with spectrophotometric measurementsrecovered from the literature, these spectra indicate that the star is a mildlymetallic K0 dwarf with Teff 5237 $\pm$ 60 K. The mass of the companion is 39.9$\pm$ 1.0 MJup and its radius is 0.81 $\pm$ 0.02 RJup, in agreement withcurrent theoretical predictions. This is the first time a bona fide brown dwarfcompanion is detected in orbit around a star of this type. The formation andorbital evolution of brown dwarf companions is briefly discussed in the lightof this new discovery.

SOPHIE velocimetry of Kepler transit candidates. VIII. KOI-205 b: a brown-dwarf companion to a K-type dwarf