Haus entered the Navy in 1869. He distinguished himself as an instructor at the Imperial and Royal Naval Academy in Fiume (now Rijeka); a product of his academic study was Oceanography and Maritime Meteorology (1891). Returning to a seagoing command, Haus was commander of a corvette during the multinational intervention in the Boxer Rebellion in China in 1900/01. After the suppression of the insurrection Haus remained in Peking (now Beijing) until 1902.

Promoted to Vizeadmiral in 1907, Haus was Austro-Hungarian envoy to the second Hague Peace Conference from May to October of that year. Appointed Flotteninspekteur (Fleet Inspector) in 1912, Haus succeeded Rudolf Montecuccoli as Marinekommandant (Navy Commander) and Chef der Marinesektion (Chief of the Naval Section of the War Ministry) on 24 February 1913.

Perhaps unaware of the gravity of the situation, Haus was notably absent during the July Crisis of 1914. At the crucial crown council of 7 July 1914, where drastic action against Serbia was decided upon, Karl Kailer von Kaltenfels stood in for his chief. Upon the outbreak of war, Haus was named Flottenkommandant (Fleet Commander). When Italy entered the war, Haus sent the battle fleet to bombard Ancona and other Italian Adriatic ports on the night of 23/24 May 1915, but for the most part he left the active fighting to the light forces—fast cruisers, destroyers and submarines.

In 1916 Haus became the only active-duty Austro-Hungarian naval officer (aside from members of the Imperial house) to be promoted to Grossadmiral (Grand Admiral). (His immediate successor, Maximilian Njegovan, was named a Grossadmiral in 1918, but on the retired list.)

Haus was succeeded as Marinekommandant and Flottenkommandant by Maximilian Njegovan and as Chef der Marinesektion by Karl Kailer von Kaltenfels; Njegovan was appointed to the latter post in April 1917 after the death of Kaltenfels. The fleet that Haus had so scrupulously maintained as a 'fleet in being' was parcelled out among the victorious powers after 1918.