The Phillies selected Kelly's contract from Triple-A Lehigh Valley on Monday, Todd Zolecki of MLB.com reports.
Kelly joins the Philadelphia bullpen as a replacement for right-hander James Norwood, who was designated for assignment in a corresponding move. The 29-year-old right-hander will head to the majors for the first time in his career after turning in a 5.00 ERA, 1.56 WHIP and 27:9 K:BB across 18 innings at Lehigh Valley.