Desir started 11 of the 12 games he played in last season, registering 50 tackles and three interceptions.
The 29-year-old Desir played three seasons with Indianapolis after he was claimed on waivers from the Seattle Seahawks.
He was taken in the fourth round by the Cleveland Browns in 2014.
Also Saturday, the Colts made official their signing of quarterback Philip Rivers, who ranks sixth in NFL history in career passing yards (59,271) and touchdowns (397). Terms were not announced, but a source told ESPN's Adam Schefter that it was a one-year, $25 million deal.
"Philip is one of the most decorated quarterbacks in the NFL and we are fortunate to add an experienced player of his caliber to our organization," Colts general manager Chris Ballard said in a statement. "His familiarity with our coaching staff and offensive system in addition to his experience were attractive qualities during our evaluation process. Philip is a fierce competitor and his veteran leadership will be crucial in the continued development of our young roster."