Wright will make $1 million if he makes the major league roster.
In 61 games last season for the Los Angeles Dodgers, Wright was 5-4 with one save and a 4.35 ERA. It was his fourth consecutive season with at least 60 appearances.
The 40-year-old Wright has pitched for 10 teams over 19 major league seasons, including Texas in 2007-08. His has a career record of 97-130 with a 4.81 ERA in 719 games (248 starts).
With the addition of Wright on Saturday, the Rangers have 62 players on their spring training roster. That includes 22 non-roster invitees.