He was elected to the Swiss Federal Council on 7 December 1977 as member of the Social Democratic Party from the canton of Neuchâtel. He handed over office on 31 December 1987. After a law degree, he became attorney-at-law in 1953. He began his political career as a member of the City Parliament of La Chaux-de-Fonds (1960–68), the Cantonal Parliament of Neuchâtel (1961–75, its president in 1969/70). Elected to the Council of States in 1975, he sat is this chamber of the Federal Parliament until his election to the Federal Council in 1977. From 1974 to 1977, he belonged to the Parliamentary Assembly of the Council of Europe and was rapporteur for the admission of Portugal. He was also chancellor of the University of Neuchâtel from 1971 to 1977.
During his time in office, he held the Political Department in 1978 and from 1979 to 1987 after it was renamed to "Federal Department of Foreign Affairs". He was President of the Confederation twice: in 1983 and in 1987. He stood for a Swiss active policy in general and in the Human rights field in particular. Aubert visited four African countries and signed a declaration against apartheid in Nigeria in 1979. He was the first Swiss foreign minister to establish contacts with the PLO leadership when he received Faruk Kaddhumi in July 1980 in Bern. He led the unsuccessful campaign to join the United Nations in 1986 (only 24% of the voters were in favour).