A long-time staple on the Patriots' offensive line, he was a part of the team's 2014 Super Bowl win and three conference titles between 2007 and 2014.
Connolly, whose contract with New England expired after the 2014 season, had one free agent visit this offseason with the Tampa Bay Buccaneers, but left without a contract.
"It's important to me to leave the game healthy," Connolly told ESPN.com. "I'm able to be here for my kids and walk away on my own terms. I feel like I got everything I could out of football in playing 10 years, winning a Super Bowl, and playing alongside some truly great players."
Connolly made 89 appearances and 71 starts over eight seasons and played across the interior of New England's offensive line. He gave up just one sack in 13 starts last year.
The move continues a reshaping of Tom Brady's offensive line, which began a year ago following the Logan Mankins deal. Now, the pressure builds for fourth-round picks Tre' Jackson and Shaq Mason, both of whom will likely have a shot at the opening.
*The latest Around The NFL Podcast discusses recent news from around the league, including the new contracts for Dez Bryant and Demaryius Thomas. *