Edwards, wearing a white No. 17 Jets jersey, caught passes from rookie Mark Sanchez, as well as backups Erik Ainge and Kevin O'Connell in early drills Thursday.
Edwards was traded from Cleveland on Wednesday for wide receiver Chansi Stuckey, linebacker Jason Trusnik and two undisclosed draft choices.
Coach Rex Ryan said Edwards will start opposite Jerricho Cotchery in the Jets' next game Monday night at Miami. The former Pro Bowl selection is in his fifth season, and gives the Jets the deep threat they were sorely missing.
Edwards had 10 receptions for 139 yards and no scores for the winless Browns.