We present a near-infrared spectrum of the close, detached white dwarf + brown dwarf binary WD 0137-349, which directly reveals the substellar companion through an excess of flux longwards of ≈1.95 μm. We best match the data with a white dwarf + L8 composite model. For ages ∼1 Gyr, the spectral type of the cool secondary is in agreement with the mass determined by Maxted et al. from radial velocity measurements (0.053 ± 0.006 M⊙), and supports an evolutionary scenario in which the brown dwarf survived a previous phase of common envelope evolution which resulted in the formation of this close binary. The brown dwarf is the lowest mass companion to a white dwarf yet found, and the lowest mass object known to have survived a common envelope phase. At 1300 < Teff < 1400 K WD 0137-349B is also the coolest known companion to a white dwarf. At a separation a= 0.65 R⊙ the hemisphere of the brown dwarf facing the 16 500 K white dwarf is being heated through irradiation. We discuss the possible effects of this additional heating, with particular relevance to those other close binaries with substellar companions, the hot Jupiters. We propose future observations to investigate the likely temperature differences between the ‘day’ and ‘night’ sides of the brown dwarf.