The team will place Britt on waivers with the expectation that he won't be claimed. Britt will then become a free agent to sign with another team.
Britt, 29, is in his ninth season and first with the Browns.
In nine games, Britt has 18 receptions for 233 yards and two touchdowns.
Britt spent the first five seasons with the Tennessee Titans, who selected him with the 30th overall pick in the 2009 draft.
Britt suffered a torn ACL early in 2011 and caused the Titans headaches with multiple off-field incidents that drew police attention.
In his third and final season with the Rams, Britt had career highs with 68 receptions and 1,002 yards.