In 1891 Dr. Branner was selected by Stanford president David Starr Jordan as professor of geology. He was then connected with the University of Arkansas. He served as vice-president of Stanford from 1898 to 1913.

In 1913, the Stanford trustees honored him with the university's presidency when Dr. Jordan was promoted to the chancellorship.

Dr. Branner retired as the university's second president in 1915 at age 65. He also resigned as head of the department of geology and mining, a post he occupied for 23 years. He was succeeded by Dr. Bailey Willis of the U.S.Geological Survey.

After retirement he was appointed by President Wilson in 1916 to investigate the cause of massive landslides affecting operations of the Panama Canal.

Dr. Branner was a recognized authority on the geology of South American republics, especially Brazil.

During his last decade he headed several expeditions into Brazil and contemplated another trip but was prevented by ill health.