The Jets agreed to send wide receiver Chansi Stuckey, special teams player Jason Trusnik and draft picks to the Browns, according to the source. ESPN.com NFL Insider Adam Schefter first reported the trade Wednesday morning.
Trusnik won AFC Special Teams Player of the Week last week and Stuckey is third on the team in receiving with 11 catches for 120 yards and a touchdown.
Edwards has struggled this year for the Browns (0-4), with 10 catches for 139 yards in the team's four games. Edwards' breakout year was 2007, when he caught 80 balls for 1,289 yards and 16 touchdowns. He regressed last year to 55 catches, 873 yards and only three scores.
Edwards made headlines off the field recently for allegedly assaulting a man outside a Cleveland nightclub. The man, Edward Givens, is a close friend of NBA star LeBron James. The NFL is investigating whether Edwards violated the league's personal conduct policy.
James said Edwards punched his friend, a promoter, outside the club around 2:30 a.m. and was critical of his actions.
"I've never crossed paths with Braylon before, but it seems like there's a little jealousy going on with Braylon and me and my friends. I have no idea why," James said. "I've never said anything to Braylon at all. But for him to do that is very childish. My friend is 130 pounds. Seriously. It's like hitting one of my kids. It doesn't make sense."