The Rangers selected Bush's contract from Triple-A Round Rock on Saturday.
Bush last pitched in the majors for the Brewers on June 30, but he was DFA'd and later released after posting a 9.58 ERA and 1.65 WHIP over 10.1 innings. He signed a minor-league deal with Texas in July and has bounced back nicely by allowing just three runs in 12.2 innings in Triple-A. Bush will give the Rangers a fresh arm in their bullpen as they attempt to lock down a spot in the playoffs. Jake Latz was optioned to Round Rock and Alex Speas was designated for assignment in corresponding moves.