Feliz, who has spent all season at Triple-A Round Rock, has been struggling to return to form after having Tommy John surgery on Aug. 1, 2012.
He was the AL Rookie of the Year in 2010, earning 40 saves to set a single-season record by a rookie. He also was an All-Star selection that season.
Feliz converted 7-of-9 save opportunities with Round Rock this season, compiling a 3.14 ERA with 31 strikeouts in 24 appearances.
To make room on the roster, the Rangers optioned reliever Ben Rowen to Triple-A. He had a 4.15 ERA in eight appearances for the Rangers.
Saunders, who was 0-5 with a 6.13 ERA in eight starts, was placed on release waivers Friday for the purpose of giving him his unconditional release.
In addition, Rangers catcher Geovany Soto, who has been on the disabled list all season after surgery to repair cartilage in his right knee, will begin a rehab assignment for Round Rock.