Milner's contract was selected by the Brewers on Saturday.
Milner gives the Brewers an additional lefty in the bullpen, with Eric Lauer heading to the minors to stretch out as a starter in a corresponding move. Milner owns a passable 4.53 ERA in 55.2 career big-league innings, though his combination of an 18.2 percent strikeout rate and an 11.1 percent walk rate is unimpressive.