The moves were announced Saturday.
Volquez is 9-10 with a 6.01 ERA in 27 starts this season. He has struck out 116 and walked 69 in 142 1-3 innings.
The 30-year-old Volquez is 53-50 with a 4.77 ERA in 153 games -- 149 starts, over nine seasons with Texas, Cincinnati and San Diego.
Brach, 27, is beginning his fourth stint with the Padres this season. In 25 relief appearances, he is 1-0 with a 3.97 ERA. Over 30 relief outings for Tucson, Brach was 3-3 with three saves and posted an ERA of 2.83.
In three seasons with the Padres, Brach is 3-6 with a 3.92 ERA.