Lewis, 35, tied for the team lead in victories (10) and led the team in starts (29) and innings (170 1/3) in 2014 after missing the previous season getting minor surgery on his elbow and a joint replaced in his hip.
He had signed a one-year minor league contract with the Rangers and earned a spot in the rotation. After a slow start, he emerged in the second half of the season. In 13 second-half starts, Lewis compiled a 3.86 ERA and saw opponents hit .251/.304/.434.
Lewis has spent seven of his nine big league seasons with the Rangers. Since 2010, he has averaged 7.86 strikeouts per nine innings, eighth best in the American League among pitchers with at least 100 starts.
The Rangers are determined to bolster their starting rotation behind Yu Darvish and Derek Holland. Getting Lewis signed gives them a veteran in the back end of the rotation. The club is expected to use a young pitcher and quite possibly trade for a veteran to finalize the five-man rotation.