Radial velocity (RV) searches for exoplanets have surveyed many of the nearest and brightest stars for long-term velocity variations indicative of a companion body. Such surveys often detect high-amplitude velocity signatures of objects that lie outside the planetary mass regime, most commonly those of a low-mass star. Such stellar companions are frequently discarded as false-alarms to the main science goals of the survey, but high-resolution imaging techniques can be employed to either directly detect or place significant constraints on the nature of the companion object. Here, we present the discovery of a compact companion to the nearby star HD~118475. Our Anglo-Australian Telescope (AAT) RV data allow the extraction of the full Keplerian orbit of the companion, found to have a minimum mass of 0.445~$M_odot$. Follow-up speckle imaging observations at the predicted time of maximum angular separation rule out a main sequence star as the source of the RV signature at the 3.3$sigma$ significance level, implying that the companion must be a low-luminosity compact object, most likely a white dwarf. We provide an isochrone analysis combined with our data that constrain the possible inclinations of the binary orbit. We discuss the eccentric orbit of the companion in the context of tidal circularization timescales and show that non-circular orbit was likely inherited from the progenitor. Finally, we emphasize the need for utilizing such an observation method to further understand the demographics of white dwarf companions around nearby stars.