Lange was born on 4 August 1942 in Otahuhu, a small industrial borough since absorbed into Auckland. He was the oldest of four children of Eric Roy Lange, a general practitioner and obstetrician and grandson of a German settler, and Phoebe Fysh Lange, who trained as a nurse in her native Tasmania before she migrated to New Zealand. The family had lived in New Zealand for so long that the original pronunciation of their surname, "lan-ge", "had all but been forgotten"; Lange himself would pronounce it as "long-ee". According to David himself, his mother's side is of Danish descent.