Gaub will be optioned to Triple-A Round Rock, which sent right-hander Yoshinori Tateyama to the Rangers to replace Feliz on the 25-man roster.
Gaub, 27, was selected in the 21st round -- 641st overall -- by the Cleveland Indians in the 2006 First-Year Player Draft. Gaub and right-handers Chris Archer and Jeff Stevens were traded to the Cubs on New Year's Eve in 2008 for Mark DeRosa.
Gaub made his Major League debut last September and allowed two runs in 2 2/3 innings across four relief appearances, striking out three and walking two.
Those four outings represent Gaub's only experience in the big leagues. He had been picked up by the Rays, who claimed him off waivers from the Cubs on April 5. Gaub went 0-1 with a 4.32 ERA and one save in 16 appearances, all out of the bullpen, for Triple-A Durham. In 187 career appearances over six seasons in the Minor Leagues, Gaub has posted a 12-13 record and a 3.65 ERA.