Webb was claimed off waivers by the Padres on Saturday.
Webb reached the majors for the first time last season, posting a 5.63 ERA in eight innings. In parts of four seasons at the Triple-A level, the 27-year-old has a 3.69 ERA with a 10.6 K/9 and a 2.5 BB/9. He'll head to Triple-A El Paso but has a decent chance of getting called up to a low-leverage role in the Padres' bullpen at some point this season.