Randy Smith, the Padres' vice president of player development and international scouting, confirmed the promotion on Wednesday.
Roach, a 22-year-old right-hander, was obtained on May 3 from the Angels in the deal that sent reliever Ernesto Frieri to Anaheim. Roach went 5-1 with a 1.74 ERA in eight games (seven starts) after the trade. All told, he went 10-1 with a 1.94 ERA in 14 games, 13 starts, pitching in the hitter-friendly California League.
"He's been unbelievably successful," Smith said of Roach, a sinkerball pitcher. "And his ball should sink more in San Antonio. He's going into a good pitching environment."
The Padres hold Roach in very high regard, and several members of the front office, including general manager Josh Byrnes, have seen him pitch in person on several occasions.
Roach is considered the 20th-best Padres prospect, according to MLB.com.