Tampa Bay, of course, will benefit from the extra pick since the Bucs are without its first-round selection, which the team gave to Oakland last year in the trade for head coach Jon Gruden.
Tampa Bay currently has six 2003 NFL Draft selections. The NFL Draft will transpire on April 26 and 27.
The Bucs were interested in re-signing Dunn last year, but the Falcons outbid the Pewter Pirates for his services, giving the former 1997 first-round pick a six-year, $28.5-million contract.
The Bucs were also hoping to receive compensatory picks for the loss of tight end Dave Moore and middle linebacker Jamie Duncan, but that didn't come to fruition.
The awarding of compensatory picks is not an exact science and is determined by how much money the departing player received from his new team, how much he contributed to his new team and what type of player the old team replaced him with. Compensatory picks may not be traded.
Scott Reynolds contributed to this story.