The Bears had tried to trade Brown after signing Julius Peppers.
The 31-year-old Brown was a fourth-round selection by the Bears in 2002 out of Florida. He was slated to make $5 million this season.
For Chicago, he appeared in 127 career games, including 107 starts, in eight seasons. He had 483 tackles, 43½ sacks, five interceptions, 16 forced fumbled and 11 fumble recoveries. He also blocked three kicks.