The Bears announced the trade Tuesday, saying they received an undisclosed draft pick from the Patriots. A league source told ESPN's Adam Schefter that Chicago will receive a sixth-round selection in the deal.
The Patriots inherit Bostic's contract, which runs through 2016. Bostic projects to have an off-the-line role in the Pats' defense, where Dont'a Hightower, Jamie Collins, Jerod Mayo and Jonathan Freeny make up the depth chart.
The acquisition of Bostic adds another layer to some of the team's planning at the position, with Hightower, Collins and Freeny also signed through 2016. Meanwhile, Mayo's contract situation is likely to be addressed following this season. He has a $4 million roster bonus due on the first day of the 2016 league year, and if the Patriots pick it up, he would count $11.4 million against the salary cap. It's highly unlikely the team will pick up the option, with Mayo now serving as the No. 3 option.
Bostic, who is 6-foot-1, 245 pounds, was the Bears' leading tackler in 2014 under the team's old regime with coach Marc Trestman. With first-year coach John Fox this season, he fell out of favor.
The Bears drafted Bostic 50th overall in the second round of the 2013 NFL draft out of the University of Florida after he ran the second-fastest 40-yard dash at that year's NFL combine. Bostic made an immediate impact as a rookie when he started nine games at middle linebacker.
The Bears switched to a 3-4 defense this past offseason, but Bostic never challenged for one of the starting inside linebacker jobs because he fell behind in the Bears' offseason program due to back problems. He later injured an ankle in the preseason and spent the first three weeks of the regular season as a game-day inactive.
Bostic worked out on a side field during practice all of last week.
ESPN.com's Mike Reiss contributed to this report.