Jon Heyman of FanRag Sports reported the deal.
Philadelphia agreed to terms with Pat Neshek on Monday, per MLB.com's Todd Zolecki, and has made a clear effort to reload its bullpen. Neshek and Hunter should provide some middle relief help to a bullpen that ranked 14th in team ERA last season.
Hector Neris should continue in the closer's role next season after recording 26 saves in 29 chances.
Hunter has found a home as a reliever after being formerly a top prospect in the Texas Rangers organization. He struggled to find consistent footing as a starter before moving to full-time relief with the Baltimore Orioles in 2013.