The Angels sent minor league pitcher Michael Clevinger to the Indians in the 1-for-1 swap.
Pestano is the fifth reliever picked up by the Angels in a trade since the beginning of July. The most notable of those moves was the acquisition of closer Huston Street from the San Diego Padres for a package of prospects on July 19.
The Angels have also brought in former Pirates closer Jason Grilli and lefties Joe Thatcher and Rich Hill, though the latter was later released.
Pestano had been one of the American League's best setup men from 2011-12, amassing 59 holds and a 2.45 ERA while striking out 160 batters in 132 innings over those two seasons. The 29-year-old has spent most of the 2014 campaign in Triple A, however, while producing a 5.00 ERA in 13 major league appearances.
Clevinger has posted a 4-3 record with a 4.31 ERA over 18 starts between Low-A Burlington and High-A Inland Empire this season. The 23-year-old righty was Anaheim's fourth-round selection in the 2011 MLB Draft.