The Cubs acquired Murray from the Astros on Saturday in exchange for first baseman Cameron Sisneros, Ari Alexander of 7 News Boston reports.
Houston designated Murray for assignment Tuesday after he allowed 11 earned runs in just 13.1 frames in the majors. He owns a 1.17 ERA and 0.79 WHIP at the Triple-A level this season, however, so the Cubs will take a chance on him and add him to their 40-man roster. The 29-year-old still has minor-league options remaining and therefore doesn't have to join the 26-man active roster immediately, though he could report directly to Chicago to provide the big club with a fresh bullpen arm.