The Reds selected Bracho's contract from Triple-A Louisville on Wednesday.
Bracho will join the Reds ahead of their series finale with the Rockies, returning to the big-league roster after being designated for assignment in late May. The right-hander has compiled a 5.06 ERA and 1.31 WHIP with four strikeouts over 5.1 innings in four appearances with Cincinnati this season. He'll help replace Casey Legumina (shoulder) in the major-league bullpen after Legumina was placed on the 15-day injured list Wednesday.