Gunnar was born in the town of Seltjarnarnes near Reykjavík, the son of actor Ævar Kvaran and the great-grandson of Einar Hjörleifsson Kvaran.
Gunnar originated from the village of Seltjarnarnes adjacent to Reykjavík, being the offspring of actor Ævar Kvaran and a descendant of Einar Hjörleifsson Kvaran.