They made room on the roster Friday by waiving long-snapper Patrick MacDonald and defensive tackle Babatunde Oshinowo.
Goodson rushed for 1,964 yards before leaving school after his junior season. He can also return kicks and impressed the Panthers with his speed in offseason workouts. Goodson will depth behind running backs DeAngelo Williams and Jonathan Stewart.
Fiammetta will compete with incumbent Brad Hoover for Carolina's starting fullback job.
The Panthers signed seventh-round choice Captain Munnerlyn earlier this week, leaving only four picks unsigned. They open training camp Aug. 2.