He graduated from the Learned School of Reykjavík in 1875 and then immediately proceeded to Copenhagen to further his studies. He studied natural history and zoology but also nourished a strong interest in geology. This was amplified in 1876 when he served as a guide for the geologist Johannes Frederik Johnstrup in an expedition to Iceland to study Askja and the volcanoes at Mývatn.
Unable to complete his studies for financial reasons Þorvaldur accepted a teaching placement at Möðruvellir in the north of Iceland in 1880 and worked there until 1885 when he became an adjunct at the Learned School. They had one child, Sigríður (1888–1903). Þóra died in 1917. In 1899, Þorvaldur resigned his position at the Learned School.
The Althing granted him a generous pension which enabled him to live in Copenhagen and work on research and writing.
In 1894, he was granted an honorary doctoral degree from the University of Copenhagen and in 1902 he was named Professor.