Johnson, a defensive end from Georgia, is the third of eight draft picks to come to terms, joining fourth-round selection Ryne Robinson and fifth-round choice Dante Rosario.
The 6-foot-2, 270-pound Johnson had 73 tackles and 14.5 sacks in three years at Georgia. Johnson had 9.5 sacks last season and was a second-team all-Southeastern Conference pick.
Johnson, who left school after his junior season, is expected to contend for significant playing time next season after the Panthers released defensive end Al Wallace in a salary cap move.
Also Monday, the Panthers waived defensive tackle Marques Thornton, who had been signed as an undrafted rookie from Texas A&M.