The deal was announced Monday.
Pastornicky was hitting .283 with one home run and 19 RBIs in 53 games at Triple-A Round Rock. He began the season in Double-A and also played for Team USA in the 2015 Pan Am Games in July.
The 25-year-old Pastornicky hit .243 in 124 games with Atlanta from 2012-14. He signed with Texas in March.