The Titans announced the moves Tuesday.
Brown tore a pectoral muscle in the Titans' season-opening win at Kansas City and had surgery Sept. 9.
The 6-foot-2, 235-pound Anderson is an eight-year veteran who has started 69 of his 110 career games. A third-round draft selection by Carolina in 2006, Anderson played seven seasons with the Panthers leading the team in tackles in 2010 and 2011. He led Chicago with 104 tackles last season and had a career-high four sacks. He signed with the Patriots in June and was released after training camp.
The Titans also added linebacker Justin Staples to the practice squad and released linebacker Brandon Copeland.