Karl Heinrich Rau was born on 23 November 1792 in Erlangen, Bavaria, the son of a Lutheran pastor and theology professor at the local university. Rau himself was educated at the University of Erlangen, obtaining his degree in 1812. He lectured in public finance at Erlangen from 1816. In 1822, he became a professor at the University of Heidelberg for the remainder of this life.

K.H. Rau's three-volume economics textbook (Lehrbuch, 1826-37), was extraordinarily successful in Germany and went through numerous editions. Rau is usually credited/blamed for introducing the tripartite division of German economic studies into economic theory , economic policy and public finance, a division which would prevail in German universities until the late 20th Century.

By virtue of his position in Heidelberg, Rau was heavily involved in the politics and administration of Grand Duchy of Baden, and was, for a time, tutor and advisor of the Grand Duke Frederick I of Baden. Rau was a champion of the liberal movement in 19th Century Germany, and was elected to the 1848 Frankfurt assembly.

Rau founded the first German economics journal, the Archiv der Politischen Oekonomie und Polizeiwissenschaft ("Archive of Political Economy and Policy Science") in 1835. Although highly influential during the main part of his career, Rau's star dimmed later on with the ascent of the German Historical School.

Rau retired from Heidelberg in 1865, after over forty years of service. He died in Heidelberg on 18 March 1870.