He was born in Kristiania as the son of Nils Lorentz Vogt and his wife Karen Johanne Holmboe.
He worked as a law clerk for the district stipendiary magistrate of Nordmøre from 1874, and was hired as a lawyer in 1876.
In 1882 he started his own law firm, and gained access to Supreme Court cases.
From 1904 to 1905 he met as a regular representative, covering for Francis Hagerup who was Prime Minister.
Vogt was also a member of public committees, including a "Commission on treatment of dangerous lunatics".