The Jets dealt the 70th overall choice to the Texans, who used it to take wide receiver Jaelen Strong. In return, the Jets received a third-round pick (82 overall), a fifth-rounder (152) and a seventh-rounder (229).
Posey, a third-round pick out of Ohio State in 2012, hasn't produced much. He has 22 career receptions for 272 yards and no touchdowns.
Jets general manager Mike Maccagnan was the Texans' director of college scouting when Posey was drafted.
In the span of an hour, the Jets added two receivers, Posey and second-round pick Devin Smith, who also happens to be from Ohio State.