The nearby Sun-like star HD 19467 shows a subtle radial velocity (RV) acceleration of -1.37+/-0.09 m/s/yr over an 16.9 year time baseline (an RV trend), hinting at the existence of a distant orbiting companion. We have obtained high-contrast adaptive optics images of the star using NIRC2 at Keck Observatory and report the direct detection of the body that causes the acceleration. The companion, HD 19467 B, is dK=12.57+/-0.09 mag fainter than its parent star (contrast ratio of 9.4e-6), has blue colors J-K_s=-0.36+/-0.14 (J-H=-0.29+/-0.15), and is separated by 1.653+/-0.004" (51.1+/-1.0 AU). Follow-up astrometric measurements obtained over an 1.1 year time baseline demonstrate physical association through common parallactic and proper motion. We calculate a firm lower-limit of m>51.9^{+3.6}_{-4.3}Mjup for the companion mass from orbital dynamics using a combination of Doppler observations and imaging. We estimate a model-dependent mass of m=56.7^{+4.6}_{-7.2}Mjup from a gyrochronological age of 4.3^{+1.0}_{-1.2} Gyr. Isochronal analysis suggests a much older age of $9±1$ Gyr, which corresponds to a mass of m=67.4^{+0.9}_{-1.5}Mjup. HD 19467 B's measured colors and absolute magnitude are consistent with a late T-dwarf [~T5-T7]. We may infer a low metallicity of [Fe/H]=-0.15+/-0.04 for the companion from its G3V parent star. HD 19467 B is the first directly imaged benchmark T-dwarf found orbiting a Sun-like star with a measured RV acceleration. ; Comment: Updated to reflect ApJ version