New general manager Kevin Towers said the move is "the first step" in improving the team's bench.
The 37-year-old had two home runs and 22 RBIs in 93 games for the Houston Astros last season. He had 14 pinch hits in 42 pinch-hit appearances
Blum, who gets $1.35 million annually, has played for five teams in parts of 12 major league seasons. He has a career .251 average with 97 home runs and 468 RBIs.
In another move, the team promoted Mike Bell from minor league coordinator to director of player development after Rico Brogna resigned.