The deal was announced Monday, an off day for the Rangers, who hold the AL's second wild card spot.
Stubbs played 51 games this season with Colorado before being designated for assignment Aug. 12, and unconditionally released Saturday. The eighth overall pick by Cincinnati in the 2006 draft, he has a .245 average in 815 at-bats for the Reds (2009-12), Cleveland (2013) and the Rockies (2014-15).
Primarily a center fielder, he had at least 30 stolen bases each season from 2010-12, including a career-high 40 in 2011.
Stubbs played on the University of Texas team that won the 2005 College World Series.