Meriweather, a first-round pick (24th overall) in the 2007 NFL Draft, has 244 total tackles and 12 interceptions over four seasons. In 2009, he had a career-high five interceptions and made the first of two straight Pro Bowls.
NFL Network's Albert Breer reported that the Patriots cut Meriweather after attempts to trade the fifth-year safety.
Meriweather joins a team that won the NFC North at 11-5 last season and made the conference title game with a defense that ranked ninth overall but just 20th against the pass.
The Bears rely heavily on takeaways and Meriweather should help in that area, considering that his 12 interceptions over the past three seasons is tied for fourth among NFL safeties.
Meriweather is known to freelance at times, but he has that history of making plays. He has also been involved in some controversy in the past.
In October 2006, while still at the University of Miami, he was part of an on-field fight with several Florida International players.
About three months earlier, he fired a gun at an assailant who had shot Miami backup safety Willie Cooper outside the house Cooper shared with Meriweather and another teammate, police said. Meriweather wasn't charged and police said he used the gun legally.
The Associated Press contributed to this report.