Jackson received a four-year deal worth $22 million, including $11 million guaranteed, according to multiple reports.
The 30-year-old Jackson was released by the Cleveland Browns on Feb. 26.
"We are pleased to announce the signing of inside linebacker D'Qwell Jackson," said Colts general manager Ryan Grigson. "He is a team-first guy that has been a very consistent producer on the field. The tempo, energy and determination he plays with are right up there with the best in this league.
"He brings a welcomed element of experience and natural leadership to our team and we are excited to add him to the strong nucleus of linebackers we currently have on our roster."
Jackson, a veteran out of Maryland, was drafted by the Browns in the second round of the 2006 NFL Draft. In eight seasons with Cleveland, he made 96 starts in 97 games, compiling 824 tackles, 11 1/2 sacks, eight interceptions, five forced fumbles and seven fumble recoveries.
Last season, Jackson recorded 141 combined tackles with 1 1/2 sacks and one interception.
Jackson is reunited in Indianapolis with former Browns coach Rob Chudzinski, who now serves as the special assistant to Colts coach Chuck Pagano.