We report the discovery of EPIC 219388192b, a transiting brown dwarf in a 5.3 day orbit around a member star of Ruprecht 147, the oldest nearby open cluster association, which was photometrically monitored by K2 during its Campaign 7. We combine the K2 time-series data with ground-based adaptive optics imaging and high-resolution spectroscopy to rule out false positive scenarios and determine the main parameters of the system. EPIC 219388192b has a radius of {R}{{b}}=0.937+/- 0.032 R Jup and mass of {M}{{b}}=36.84+/- 0.97 M Jup, yielding a mean density of 59.6+/- 7.6 {{g}} {{cm}}-3. The host star is nearly a solar twin with mass {M}\star =1.01+/- 0.04 M ⊙, radius {R}\star =1.01+/- 0.03 R ⊙, effective temperature T eff = 5850 ± 85 K, and iron abundance [Fe/H] = 0.03 ± 0.08 dex. Its age, spectroscopic distance, and reddening are consistent with those of Ruprecht 147, corroborating its cluster membership. EPIC 219388192b is the first mature brown dwarf with precise determinations of mass, radius, and age, and serves as benchmark for evolutionary models in the substellar regime.