Born on April 6, 1837, near Cologne, Prussia,[1] Finkelnburg immigrated to the United States in 1848 with his parents, who settled in St. Charles, Missouri.

[1] He was admitted to the bar and entered private practice in St. Louis, Missouri starting in 1860.

[1] He was a member of the Missouri House of Representatives from 1864 to 1868, serving as Speaker pro tempore in 1868.

[2] Finkelnburg received a recess appointment from President Theodore Roosevelt on May 20, 1905, to a seat on the United States District Court for the Eastern District of Missouri vacated by Judge Elmer B. Adams.

[1] He was confirmed by the United States Senate on December 12, 1905, and received his commission the same day.