Crockett agreed to a minor-league contract with the Reds on Monday, Zach Buchanan of the Cincinnati Enquirer reports.
The deal includes an invitation to spring training. It's been a busy couple of weeks for Crockett, as he was non-tendered by the Reds last week just days after the team claimed him off waivers from the Indians. The 25-year-old southpaw spent most of his time with Triple-A Columbus last season but has made major-league appearances in each of the last four seasons, compiling a respectable 3.12 FIP over 65.1 major-league innings during that stretch. Look for him to compete for an Opening Day spot in the Reds' bullpen.