Bloomquist became a free agent when he turned down his end of a $1.1 million mutual option on Nov. 1. He signed with Arizona last offseason and became the everyday shortstop when Stephen Drew broke his ankle on July 20.
Bloomquist hit .266 with four homers and 26 RBIs in 97 games last season.
Arizona also signed right-hander Chris Jakubauskas to a minor league deal. The 32-year-old pitched 32 games for Baltimore last season, including six starts, and went 2-2 with a 5.72 ERA.
Jakubauskas is 8-10 with a 5.58 ERA in three major league seasons with Seattle, Pittsburgh and the Orioles.