Born and educated in Copenhagen, he became a schoolmaster, and ultimately in 1883 a professor at the University of Copenhagen. He was strongly influenced by Søren Kierkegaard in his early development, but later became a positivist, retaining and combining with it the spirit and method of practical psychology and the critical school.
His best-known work is perhaps his Den nyere Filosofis Historie (1894), translated into English from the German edition (1895) by B.E. Meyer as History of Modern Philosophy (2 vols., 1900), a work intended by him to supplement and correct that of Hans Brøchner, to whom it is dedicated. His Psychology, the Problems of Philosophy (1905) and Philosophy of Religion (1906) also have appeared in English.
Among Høffding's other writings, practically all of which have been translated into German, are: Den engelske Filosofi i vor Tid (1874); Etik (1876); Psychologi i Omrids paa Grundlag of Erfaring (ed. 1892); Psykologiske Undersøgelser (1889); Charles Darwin (1889); Kontinuiteten i Kants filosofiske Udviklingsgang (1893); Det psykologiske Grundlag for logiske Domme (1899); Rousseau und seine Philosophie (1901); Mindre Arbejder (1899).