He was signed by the St. Louis Cardinals as an amateur free agent in 2012, and made his Major League Baseball (MLB) debut with the team in 2016.

[4] There, it would be much easier to gain the attention of scouts to increase his chances of signing with a Major League Baseball (MLB) team as a free agent[3] rather than be selected through the amateur draft had he remained in the United States.

[4] In the Dominican Republic, Reyes lived with each of his grandmothers in San Cristóbal, enabling him to gain residency and the notice of scouts, known colloquially as buscones.

Cardinals general manager John Mozeliak commented that Reyes' athleticism was one important factor that caused the team to consider the young pitcher.

[11] The beneficiary of a late growth spurt, Reyes grew to a height of 6 ft 4 in (1.93 m) and began throwing at up to 100 miles per hour (160 km/h) in Single–A.

On June 25, Reyes was selected to represent the World Team in the All-Star Futures Game after leading all of the minor leagues with a ratio of 13.4 strikeouts per nine innings pitched (SO/9).

[15] He totaled a 5–7 record and 2.49 ERA over 22 starts in 2015, striking out 151 in 101+1⁄3 innings while allowing a .197 opposing batting average.

[17] Baseball America also selected Reyes for the high Class-A minor leagues All-Star team for the 2015 season.

[21] Reyes was activated from his suspension on May 22 to make his first start for the Memphis Redbirds of the Triple–A Pacific Coast League.

[25] The Cardinals purchased Reyes' contract on August 9, 2016, and added him to the major league roster to serve as a relief pitcher.

[29] After five appearances and 9+1⁄3 innings in relief with 13 strikeouts and no runs surrendered, he made his first MLB start on August 27 against the Oakland Athletics.

The first run charged to Reyes in his major league career occurred when reliever Zach Duke walked Khris Davis with the bases loaded to score Bruce Maxwell in the fifth, ending 14 consecutive scoreless innings.

In four total rehab starts between Springfield, the Peoria Chiefs, Palm Beach Cardinals and Memphis, he pitched 23 scoreless innings in which he struck out 44, walked seven, and gave up only seven hits.

[39] Making his first major league appearance since September 29, 2016, Reyes pitched four scoreless innings, allowing three hits while walking two and striking out two.

[40] On June 6, Reyes underwent surgery for a torn tendon in his lat muscle, effectively ending his season.

However, in his first three innings of the year, he allowed five runs and six walks and was ultimately optioned to the Class AAA Memphis Redbirds on April 7.

[46] In the 2021 National League Wild Card Game, Reyes gave up a two-out, two-run, walk-off home run to Chris Taylor in the bottom of the ninth inning.

[47] Reyes was placed on the 60-day injured list to begin the season on March 25, 2022, after struggling with a shoulder issue in Spring Training and receiving a stem-cell injection.

The curveball has been called a "wipeout" pitch with a vertical falling pattern following the points from "12-to-6" on the clock, making it equally difficult for batters to hit well.