Also on Tuesday, the club waived linebacker Worrell Williams. Additionally, defensive lineman Lionel Dalton was signed by Miami to its active roster.
Brown (6-foot-3, 250 pounds) is a third-year player who spent the previous two years with Cleveland, playing in five games (0 starts) after signing with the Browns as a college free agent from Mississippi State University in 2008.
A four-year letterman for the Bulldogs, he played in 44 games (30 starts) and totaled 170 tackles, 18.5 sacks, three forced fumbles and one fumble recovery during his collegiate career.
Brown attended Hillcrest High School in Tuscaloosa, Ala., and was born on March 27, 1986.
Jeff Stehle (6-foot-6, 310 pounds) is a rookie defensive lineman who was originally signed by the Broncos as a college free agent from the University of Wisconsin on April 26, before being waived on Sept. 4.