Spectroscopic observations of the fast X-ray transient and superluminal jet source SAX J1819.3-2525 (V4641 Sgr) reveal a best fitting period of P spect=2.81678+/- 0.00056 days and a semiamplitude of K2=211.0+/- 3.1 km s-1. The optical mass function is f(M)=2.74+/- 0.12 Msun. We find a photometric period of P photo=2.81730 +/- 0.00001 days using a light curve measured from photographic plates. The folded light curve resembles an ellipsoidal light curve with two maxima of roughly equal height and two minima of unequal depth per orbital cycle. For the secondary star we find T eff=10500 +/- 200 K, log g=3.5+/- 0.1, and V rotsin i=123+/- 4 km s-1 (1σ errors). Assuming synchronous rotation, our measured value of the projected rotational velocity implies a mass ratio of Q≡ M1/M_2=1.50+/- 0.08 (1σ ). The lack of X-ray eclipses implies an upper limit to the inclination of i<= 70.7o. On the other hand, the large amplitude of the folded light curve (≈ 0.5 mag) implies a large inclination (i≳ 60o). Using the above mass function, mass ratio, and inclination range, the mass of the compact object is in the range 8.73 <= M1 <= 11.70 Msun and the mass of the secondary star is in the range 5.49 <= M2<= 8.14 Msun (90% confidence). The mass of the compact object is well above the maximum mass of a stable neutron star and we conclude that V4641 Sgr contains a black hole. The secondary is by far the most massive, the hottest, and the most luminous secondary of the dynamically confirmed black hole X-ray transients. Assuming E(B-V)=0.32+/- 0.10, we find a distance 7.40 <= d <= 12.31 kpc (90% confidence). This large distance and the high proper motions observed for the radio counterpart make V4641 Sgr by far the most superluminal galactic source known with an apparent expansion velocity of ≳ 9.5c and a bulk Lorentz factor of Γ ≳ 9.5, assuming the jet was ejected during the main X-ray flare.