Cahill made one start with High-A Visalia before moving to Reno. He had a 4.45 ERA in 30-1/3 innings in the minors, with 20 walks and 27 strikeouts.
Cahill was send to the minors with the understanding he would be brought back to the majors at a specified time, GM Kevin Towers previously said. Cahill is under contract for next season for $12.3 million.
The Diamondbacks will follow Cahill in their post-All-Star break rotation with left-hander Wade Miley and right-hander Josh Collmenter against the Cubs. Lefty Vidal Nuno and righty Chase Anderson will start against the Tigers next week.
Bolsinger, in two stints in the rotation this season, had a 5.50 ERA in 52-1/3 innings.