Osterhaus was appointed Midshipman on 22 September 1865 and received his commission as an Ensign on 13 July 1871.

He was commissioned Master, 12 February 1874; Lieutenant 13 March 1880; Lieutenant Commander 3 March 1899; Commander 2 July 1901; Captain 19 February 1906; Rear Admiral 4 December 1909 and was placed on the retired list 15 June 1913.

He was captain of the battleship Connecticut (BB-18) as part of the Great White Fleet which was a United States Navy force that completed a circumnavigation of the world from December 16, 1907, to February 22, 1909 by order of U.S. President Theodore Roosevelt.

Roosevelt sought to demonstrate growing American military power and blue-water navy capability.

During World War I he received the Navy Cross for services in the Office of Naval Districts.