Brunnström served at the consulate-general in Calcutta in 1937, was the acting consul general there in 1938, attaché in Paris in 1939, Oslo in 1940 and was second legation secretary in Washington, D.C. in 1941. He was the acting charge d'affaires in Mexico City in 1942, legation secretary in Rio de Janeiro in 1943 and in Buenos Aires in 1944 and the first secretary at the Foreign Ministry in 1944. Brunnström was then director of the Foreign Ministry's Maritime Bureau (Utrikesdepartementets sjöfartsbyrå) 1946-48, first secretary of the mission in Washington, D.C. in 1948 and in Buenos Aires in 1949 as well as director at the Foreign Ministry in 1954.