Watson, 32, spent the last three seasons as the starting tight end for the Browns. He caught 49 passes for 501 yards and three touchdowns last year in Cleveland.
Prior to joining the Browns, Watson spent six years with the New England Patriots.
For more NFL news, rumors and analysis, follow@EyeOnNFL on Twitter, subscribe to ourRSS Feed, watch Pro Football 360 daily at 3 p.m. ET and NFL newsletter. You can also follow Evan Hilbert @evanhilbert.