The Cowboys released Woods after selecting three defensive linemen, including a pair of tackles, in the NFL draft.
Woods started 32 games over three seasons in Dallas. Known as a space-eater up front, he notched 80 tackles, eight quarterback hits, and 2.5 sacks for the Cowboys.
Indianapolis has now added a pair of notable free agents following the draft in Woods and former Kansas City Chiefs left tackle Eric Fisher. Aside from acquiring quarterback Carson Wentz, the Colts were fairly quiet in the pre-draft phase of free agency.