Gilbert, a former Oklahoma State cornerback and kick returner, was picked No. 8 overall in the 2014 NFL Draft but struggled in Cleveland. The Browns will receive a sixth-round pick in the 2018 draft.
Gilbert started three games in two seasons in Cleveland.
At OSU, Gilbert was a finalist for the Jim Thorpe Award for the nation's best defensive back and set a Big 12 career record for kick returns in a season with six.
Gilbert totaled 182 tackles as a Cowboy with five interceptions.
The trade comes an hour before OSU's season opener against Southeastern Louisiana at Boone Pickens Stadium.