 Vogt was born in Kristiania as the son of professor of metallurgy Johan Herman Lie Vogt (1858–1932) and his wife Martha Johanne Abigael Kinck (1861–1908).He was the brother of geologist Thorolf Vogt, Norwegian Water Resources and Energy director Fredrik Vogt and economist Johan Herman Vogt.His uncle Ragnar Vogt was a professor of medicine; as was his second cousin, who was named Jørgen Herman Vogt as well.