Wüst became a privatdozent at the age of 25, and by the age of 31 he had become a professor. He joined the Nazi Party in 1933, and subsequently became an agent of the Sicherheitsdienst. In early 1935, Wüst was made Professor of Aryan Culture and Linguistics and Dean of the Faculty of Philosophy at the University of Munich. Prominent students of Wüst at the University of Munich include Davud Monshizadeh and Karl Hoffmann.[2] He was admitted to the Schutzstaffel in 1936, and was made President of the Ahnenerbe in 1937. As such he became the de facto leader of the Ahnenerbe under the nominal chief Heinrich Himmler. As the leader of Ahnenerbe, Wüst played a leading role in the management of universities in Nazi Germany. He was made Rector at the University of Munich in 1941. In 1943, Wüst participated in the development and spread of Nazi propaganda in the Middle East, which attempted to make Arabs and Muslims sympathetic to Adolf Hitler. Wüst was directly involved in the arrest of Hans and Sophie Scholl.
After the end of World War II in Europe, Wüst was arrested by the Office of Military Government, United States. He was interned at Dachau until 1948, and fired from the University of Munich in 1946. On 9 November 1949, the denazification courts sentenced Wüst to three years of hard labour and confiscated half of his property. He also lost his right to exercise his profession, but was later able to publish on the subject of Indology. He regained the title of Professor in 1951, but never chaired a department at a German university again. Wüst died in Munich on 21 March 1993.