Eligible for arbitration for the first time, Tolleson got a raise of more than $2.75 million with Monday's deal. He made $519,700 last year, slightly above the major league minimum.
When the Rangers and the pitcher traded figures 10 days earlier, Tolleson asked for $3.9 million and the club offered $2.6 million. They settled $25,000 above the midpoint.
Tolleson had 35 saves in 37 chances last season, though he didn't become the closer until late May for the AL West champions. The 27-year-old right-hander was 6-4 with a 2.99 ERA in 73 appearances.