Gaddis had his contract selected by Cleveland and is scheduled to start Friday's game against the Astros.
The 24-year-old was promoted from Double-A Akron to Triple-A Columbus in July and will now make his way to the majors for the first time. Gaddis has a 4.07 ERA, 1.16 WHIP and 114:31 K:BB over 86.1 innings between Akron and Columbus this season. If the right-hander pitches well in his debut he could make another turn or two through the rotation, depending when Aaron Civale (wrist) is able to return from the injured list.