Stephenson was claimed off waivers by the Pirates on Saturday, Alex Stumpf of DKPittsburghSports.com reports.
Stephenson made 45 relief appearances for the Rockies this year and posted a 6.04 ERA and 1.48 WHIP in 44.2 innings before being designated for assignment Thursday. He's expected to join the Pirates' bullpen and should serve mainly as a middle reliever for his new club.