His deal includes $2.5 million in salary in 2020 and 2021, plus a $3-million option with a $500,000 buyout for 2022, according to Evan Grant of the Dallas Morning News.
Rodriguez, 28, spent parts of the last two seasons with the Chunichi Dragons in Japan. He posted a 1.85 ERA in 87 2/3 innings during his stint overseas.
The southpaw reliever last pitched in the majors during the 2017 season as a member of the Philadelphia Phillies. He signed with the Baltimore Orioles the following offseason but was released in 2018 after posting a 4.56 ERA (2.77 FIP) in 49 1/3 innings at Triple-A.