The 6-3, 205-pound Johnson played collegiately at Western Illinois after transferring from Northwestern. He spent the first part of his rookie season with the CFL's Calgary Stampeders.
Cochran was placed on injured reserve after dislocating his left shoulder.
In another roster move, the Packers signed tight end Luther Broughton as a free agent Sunday.
Broughton, 6-0, 255 pounds, was drafted by Philadelphia as a fifth-rounder in 1997 out of Furman.
He is a six-year pro, serving stints with the Eagles and Panthers, where he played in 15 games in 2001. He was picked up by the Bears during 2002 training camp, but was out of football during the regular season.
In a related transaction, tight end Joey Knapp was waived/injured (hamstring), the team announced.