He became a second lieutenant in the Swedish Navy in 1899 and sub-lieutenant in 1901. Tamm was promoted to lieutenant in 1907 and was adjutant and librarian at Sjökrigsskolan as well as teacher in law of war and maritime law from 1907 to 1910 and in naval warfare from 1910. He was adjutant at the Command Expedition of the Ministry for Naval Affairs from 1911.
Tamm was naval attaché in Berlin and Copenhagen from 1914 to 1917, secretary in Royal Swedish Society of Naval Sciences from 1918 to 1921 and was head of Sjökrigsskolan from 1921 to 1925.
He was promoted to flag captain in 1930 and was an expert at the World Disarmament Conference in Geneva in 1932. Tamm was head of the Command Expedition of the Ministry for Naval Affairs from 1931 to 1933 and Chief of the Coastal Fleet (Kustflottan) from 1933 to 1939.
He was promoted to vice admiral in 1939 and was Chief of the Navy from 1939 to 1945. He was appointed admiral in the reserve in 1947, two years after he left active service.
Tamm was then head of department at the Naval Staff in 1926, was promoted to captain in 1927 and was a member of the Defense Committee in 1928 and 1929. In 1914, Tamm became a member of the Royal Swedish Society of Naval Sciences (honorary member in 1933) and in 1925 he became a member of the Royal Swedish Academy of War Sciences.