Maddux will be reunited with his brother Mike, who has been the Rangers' pitching coach for the last three seasons.
The four-time Cy Young Award winner will serve as an extra instructor for both the minor and major league staffs during spring training and will visit the club's farm affiliates during the regular season.
"We're excited to add Greg to our group and look forward to him contributing to the development of our young pitchers," said Rangers general manager Jon Daniels.
Maddux, 45, won four consecutive Cy Young Awards from 1992-95, becoming the first pitcher in history to accomplish the feat. He compiled a 355-227 record, won 18 Gold Glove Awards and was selected to the eight All-Star teams during his 23 Major League seasons with the Braves, Cubs, Dodgers and Padres.