He was born in Solund as the son of Edvard Sverdrup and his wife Agnes, née Vollan. His father was stationed in Solund as a vicar. Einar Sverdrup was the grandson of vicar and politician Harald Ulrik Sverdrup, a grandnephew of Johan Sverdrup, a nephew of politician Jakob Sverdrup and theologian Georg Sverdrup, a half-brother of oceanographer Harald Ulrik Sverdrup, Jr., and a brother of engineer and military officer Leif Sverdrup and women's rights activist Mimi Sverdrup Lunden. On the maternal side he was a grandson of Ole Vollan, and a first cousin of Harald and Nordahl Grieg.