The right-hander went 3-1 with a 3.16 ERA in eight games -- seven starts -- in 2012 after moving to the rotation.
The 24-year-old will open the 2013 season on the disabled list as he continues to rehab from Tommy John surgery.
As the Rangers' closer in 2010 and 2011, Feliz recorded 72 saves in 134 appearances, and earned American League Rookie of the Year honors in '10. He is 10-7 with a 2.67 ERA and 74 saves in his career with the Rangers.
With Feliz's agreement, outfielder David Murphy is the only Rangers player eligible for salary arbitration.
Quinn Roberts is a reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.