Axford was the closer for the Brewers from 2010 to 2012. In 2011, he recorded 46 saves and struck out 86 batters in 73 2/3 innings. He finished ninth in Cy Young voting and 17th in the MVP race that season.
The Brewers traded him to the Cardinals in August 2013. He made six appearances in the playoffs for St. Louis, allowing just one run.
Axford, 31, made 49 appearances for Cleveland this season, recording ten saves. In 43 2/3 innings, he has 51 strikeouts and 30 walks.
The Pirates sit 1.5 games behind the Brewers in the NL Central, but hold the first of the NL's two Wild Card spots.
- Dan Gartland