Poteat, an unrestricted free agent, had two interceptions, a sack, two forced fumbles and a fumble recovery last season for the New York Jets.
A favorite of new Browns coach Eric Mangini, Poteat spent the last three seasons with the Jets. All four of his career interceptions have come in the last two seasons.
The 31-year-old Poteat was a third-round draft choice of the Pittsburgh Steelers in 2000 and played three seasons there. He has also played with Tampa Bay and New England.