Born in London to a Saxon merchant, his family relocated to Prague when he was three, then to Vienna when he was 14. Interested in geology at a young age, he published his first paper (on the geology of Carlsbad) when he was 19.
By 1857 he was a professor of geology at the University of Vienna, and from there he gradually developed views on the connection between Africa and Europe; eventually he came to the conclusion that the Alps to the north were once at the bottom of an ocean, of which the Mediterranean was a remnant. While not quite correct (mostly because plate tectonics had not yet been discovered -- he used the earlier geosyncline theory), this is close enough to the truth that he is credited with discovering the Tethys Ocean, which he named in 1893.
His other major discovery was that the glossopteris fern was found in fossils in South America, Africa, and India (as well as Antarctica, though Suess did not know this). His explanation was that the three lands were once connected into a supercontinent, which he named Gondwanaland. Again, this is not quite correct: Suess believed that the oceans flooded the spaces currently between those lands, when in fact the lands drifted apart. Still, it is similar enough to what is currently believed that his naming has stuck.
Suess is considered one of precursors of ecology. He published a comprehensive synthesis of his ideas in 1885-1901, entitled Das Antlitz der Erde (translated into English as The Face of the Earth), which was a popular textbook for many years. In this work Suess also introduced the concept of the biosphere, which was later extended by Vladimir I. Vernadsky in 1926.