Jackson received a four-year deal worth $22 million, including $11 million guaranteed, a league source told ESPN NFL Insider Adam Schefter.
"It wasn't a financial decision, it was a decision to be around a good group of guys first and foremost and the chance to get to a Super Bowl,'' Jackson said. "It wasn't about money.''
Colts owner Jim Irsay and the team's Twitter account welcomed Jackson in separate tweets Thursday morning.
Welcome to the Colts, D'Qwell!
- Jim Irsay (@JimIrsay) March 6, 2014
- Indianapolis Colts (@Colts) March 6, 2014
The Cleveland Browns cut ties with Jackson, who was due a $4.1 million roster bonus this month, on Feb. 26. He made visits to several teams in the days after he was released.
In joining the Colts, Jackson is reunited with former Browns coach Rob Chudzinski, who was hired by Indianapolis to assist coach Chuck Pagano after being fired by Cleveland after just one season at the helm.
"We are pleased to announce the signing of inside linebacker D'Qwell Jackson," general manager Ryan Grigson said in a statement. "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 also is looking forward to playing with defensive end 33-year-old Robert Mathis, who recorded 19.5 sacks last season.
"I want to know how he found the youth somewhere. I'm excited to pick his brain. I've watched him throughout his glory days and he's still having his glory days,'' Jackson said. "I've just got a good feeling in this situation.''
The 30-year-old Jackson has made 96 starts in eight seasons. He led the Browns with 139 tackles in 2013 and has 418 since 2011, fourth most of any player in that span.
Jackson overcame two serious chest injuries earlier in his career. He missed most of two seasons but recovered and was a mainstay on Cleveland's defense despite playing under four head coaches and four defensive coordinators.
The Associated Press contributed to this report.