Hart was claimed off waivers by the Brewers on Thursday and subsequently optioned to Triple-A San Antonio.
Hart spent the majority of the 2018 campaign with Triple-A Norfolk, compiling a 2.41 ERA and 45:10 K:BB across 41 innings (three starts, 29 relief appearances). The 28-year-old has appeared in the majors each of the last three seasons, notching a combined 3.43 ERA and 54:31 K:BB in 81.1 innings of relief.