We present the final calibration of the Hopkins Ultraviolet Telescope (HUT) for its flight during the Astro-1 space shuttle mission in 1990 December. The calibration is defined by a comparison between an observation obtained in flight of the hot DA white dwarf G191-B2B and the model atmosphere for this star calculated by P. Bergeron. We also present the postflight laboratory calibration of the HUT sensitivity, which we find to be in excellent agreement with the white dwarf calibration. The ratio of the white dwarf to the laboratory effective area calibration has a mean value of 1.0044 over the wavelength range 912-1840 Angstrom, a slope of 7.61 x 10(-6) Angstrom(-1) (which corresponds to a relative difference of only 0.35% at either end of the spectrum), and fluctuations about the mean value with an rms amplitude of 3%. The uncertainties in the laboratory calibration are 4% for the overall normalization, 5% relative to the mean on wavelength scales of 50 to several hundred Angstrom, and an uncertainty in the overall slope that corresponds to 1% at 1840 Angstrom and that increases smoothly to 3% at 912 Angstrom. These results validate the use of white dwarf models as absolute flux standards in the far-ultraviolet, especially for wavelengths shortward of Ly alpha, where previous experiments often disagreed by large factors. In particular, the normalization and wavelength dependence of the sensitivity calibration adopted by the Hubble Space Telescope Faint Object Spectrograph is confirmed to within the uncertainties of our laboratory calibration, while the normalization of the IUE final calibration is found to be low by an amount just exceeding our 1 sigma uncertainty. Fits to the spectra of both G191-B2B and the hot DA white dwarf HZ 43 yield effective temperatures and surface gravities in good agreement with values derived from Balmer line profiles. We also present a comparison with Voyager spectra for the stars G191-B2B, HZ 43 ED +28 degrees 4211, pi Aqr, and HD 25443. When averaged over broad bands (912-1050 Angstrom, 1050-1180 Angstrom), fluxes from the two instruments typically agree to within 10%.