Axford, 31, has pitched to a 3.92 ERA (96 ERA+) and 1.70 K/BB ratio in 43 2/3 innings for Cleveland this season. For his career, he owns an ERA of 3.38 (118 ERA+) across parts of six major-league seasons. In 2011 with the Brewers, Axford led the NL in saves and finished ninth in the NL Cy Young balloting. He's owed the balance of a $4.5-million salary for 2014.
Ernesto Frieri earlier on Thursday accepted an assignment to Triple-A, so that left the Pirates with a vacancy in the bullpen.