From 1801 to 1804, Krug was professor of philosophy at Frankfurt (Oder), after which he succeeded Immanuel Kant in the chair of logic and metaphysics at the University of Königsberg. From 1809 till his death he was professor of philosophy at the University of Leipzig. He fought in the War of Liberation (1813–14) as captain of mounted chasseurs. He became Kant's successor at the University of Königsberg after the faculty of philosophy elected him to Kant's chair of logic and metaphysics.