Bush spent the last five seasons with Milwaukee. He was 8-13 with a 4.54 ERA in 32 games (31 starts) last year.
He made at least 29 starts in four of the last five seasons. He won 12 games in both 2006 and 2007 when Rangers pitching coach Mike Maddux held the same job with the Brewers.
In 193 games over seven major league seasons with Toronto (2004-05) and Milwaukee (2006-10), the 31-year-old Bush is 56-68 with a 4.66 ERA.
With the addition of Bush on Sunday, the Rangers have 54 players on their spring training roster.