Brum's first major posts were as minister of public education (1913–15) and minister of foreign affairs (1914–15). He served on the commission that revised the Uruguayan constitution (April–June 1917) and was the first president of the country under the new constitution (March 19, 1919–March 19, 1923). He became director of the prominent publication El Día (1923–29; “The Day”) and was president of the Council of National Administration (1929–31).

Among Brum's many publications are La doctrina del arbitraje amplio (1915; “The Doctrine of Absolute Arbitration”), La paz de América (1923; “The Peace of America”), and Los derechos de la mujer (1923; “The Rights of Women”). He was responsible for instituting free and compulsory primary education, for founding public libraries, and for distributing free food to the unemployed and destitute, in addition to enhancing his country's prestige in the field of foreign relations.