Gravgaard, 30, has 18 international caps, scoring five goals.
The qualified accountant was a relatively late entrant to the professional game, joining Viborg from local side Randers in 2002.
He earned a move to Copenhagen three years later and got his first cap soon afterwards.
Ligue 1
Lyon and Marseille dispute Ben Arfa deal
30/06/2008 AT 12:50
Gravgaard - who can also play as a striker - hit the headlines in June 2007 when, during a Euro 2008 qualifier between Denmark and Sweden, he pulled a drunken fan away from referee Herbert Fandel during the now infamous on-pitch attack.
Nantes won promotion from Ligue 2 last season after finishing second, behind Le Havre.
Ligue 1
PSG making Digard "go mad"
30/06/2008 AT 12:01
Ligue 1
Marseille confident on Ben Arfa
29/06/2008 AT 13:15