Ashby's contract was selected by the Brewers on Wednesday.
Ashby will make his major-league debut as the starter in Wednesday's matchup against the Cubs, but the Brewers plan to have a bullpen game in the series finale. The southpaw has served as a reliever recently and hasn't pitched more than two innings in nearly a month. Since moving to the bullpen with the Triple-A club, Ashby has posted an 8.71 ERA and 2.03 WHIP in 10.1 innings.