From 1931 to 1959 he held a chair for classical philology at the University of Hamburg where he established the Thesaurus Linguae Graecae research centre in 1944.
In 1953, the Europa-Kolleg Hamburg, an institution promoting research and postgraduate education in the field of European integration, was founded on Snell's initiative.
Since 1989, the Mommsen Society awards the Bruno Snell Prize to young classical scholars.
His book, The Discovery of the Mind: The Greek Origins of European Thought (Die Entdeckung des Geistes, Hamburg, 1946, trans.
Rosenmeyer, 1953) argues that the development of Greek literature from Homer to Aristophanes and Plato shows a gradual self-discovery of an inner mental life.