The Marlins claimed Veneziano off waivers from the Royals on Tuesday.
The left-hander was designated for assignment by Kansas City over the weekend, and Miami scooped him up to bolster its bullpen depth. Veneziano has made just two big-league appearances this season and has a 4.80 ERA, 1.47 WHIP and 76:42 K:BB across 31 outings (14 starts) at Triple-A.