Reyes had Tommy John surgery on his pitching elbow, and he hasn't pitched in the majors since Sept. 29, 2016.
In four rehab starts, Reyes struck out 44 batters in 23 scoreless innings.
The hard-throwing Reyes was one of St. Louis' top prospects when he made his debut during the 2016 season. He finished that year 4-1 with a 1.57 ERA and 52 strikeouts in 46 major league innings.
In corresponding moves, the Cardinals optioned right-hander Mike Mayers to Triple-A Memphis and transferred right-hander Dominic Leone from the 10-day disabled list to the 60-day DL to make room on the 40-man roster for Reyes.
The Associated Press contributed to this report.