The 30-year-old Gagne, who has battled injuries over the last two seasons with the Los Angeles Dodgers, could earn another $5 million by hitting incentive targets.
Gagne, a right-hander, had 152 saves as the Dodgers' closer in 2002-2004 but pitched in only 16 games over the past two years after being slowed by elbow and back injuries.
Akinori Otsuka had 32 saves and a 2.11 ERA as the Rangers' closer last season but is expected to be the set-up man for Gagne this year.
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Gagne won the Cy Young Award in 2003 as the National League's best pitcher when he converted all 55 save opportunities and had a 1.20 ERA in 77 games for the Dodgers.
During one stretch from 2002 through 2004, Gagne converted a major league-record 84 consecutive save opportunities.
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