The 30-year-old Axford, who was non-tendered by the St. Louis Cardinals, pitched 54 2/3 innings in 2013 for the Milwaukee Brewers, but he was removed from the closer role after six blown saves and was traded to the Cardinals in August.
In 10 1/3 regular-season innings for St. Louis, Axford gave up two earned runs, walked three and struck out 11 with a 1.74 ERA.
Axford was called upon six times in the postseason, striking out four and giving up one earned run against the Pittsburgh Pirates and Los Angeles Dodgers. In two World Series appearances, he didn't allow a hit and struck out five in 2 1/3 innings.
His seven total blown saves in 2013 were the second-most of his career.
Axford reportedly had drawn interest from several teams this offseason, including the Chicago Cubs.
Information from The Associated Press and ESPN The Magazine's Buster Olney was used in this report.