Volstead was born in Kenyon, Goodhue County, Minnesota, to Norwegian-American parents Jon Einertson Vraalstad (John Vrolstad), a distant relative of Queen Sonja of Norway,[citation needed] and wife Dorothea Mathea Lillo.

According to his obituary in a 1947 edition of the Minneapolis Star, he first practiced law in Grantsburg, Wisconsin, before moving to Granite Falls in 1886.

Although often considered the author of the Volstead Act, he collaborated with Wayne Wheeler of the Anti-Saloon League, who conceived and largely drafted the bill.

Upon repeal of Prohibition in 1933, Volstead returned to Granite Falls, Minnesota, where he resumed the private practice of law.

Volstead's former home, located at 163 Ninth Avenue, Granite Falls, Minnesota, is a National Historic Landmark.