Kelley was claimed off waivers by the Phillies on Monday, Todd Zolecki of MLB.com reports.
Kelley made his big-league debut for Boston last season, struggling to an 8.64 ERA and a 6:5 K:BB in 8.1 innings. He doesn't have much left to prove at the Triple-A level, however, as he owns a career 1.73 ERA there over 88.2 frames.