The Rangers announced the agreement with the 2018 NL All-Star on Wednesday. Outfielder Adolis Garcia was designated for assignment to make room on their roster.
Foltynewicz, 29, made only one start for Atlanta last season, allowing six runs in 3⅓ innings in a loss at Tampa Bay. He spent the rest of the season in the Braves' alternate training site.
Before that, Foltynewicz was 40-34 in 103 games for the Braves from 2016 to '19. His best season was his All-Star year in 2018, when he was 13-10 with a 2.85 ERA in 31 starts. He started four of Atlanta's nine NL Division Series games in 2018-10.
He was a first-round pick in 2010 by the Houston Astros and made his big league debut with them in 2014. He was traded the following offseason to the Braves. He has a 44-42 record and 4.33 ERA in 118 starts and 20 relief appearances in his big league career.