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Hughes was the 10th overall pick in the 2022 draft. He was 6-5 with a 6.21 ERA in 14 starts across Single and Double A this season.
The Dominican Republic-born Vargas was 6-3 with a 4.22 ERA at Single A this season.
And Cox, a second-round pick last year, was 1-0 with a 7.26 ERA at Single A this season.
Earlier this month, the Rockies said major league right-hander Antonio Senzatela would have Tommy John surgery on his pitching elbow, and the team said Monday that the procedure also will take place this week. He made only two starts this season (0-1, 4.70 ERA).
Texas Rangers team physician Dr. Keith Meister will perform the surgeries on all four pitchers.