Leu was born in Münster. He was a pupil of Johann Wilhelm Schirmer, a landscape painter of the Düsseldorf school.
Leu travelled in Norway in 1843 and 1847, and later travelled widely in the Alps. His Norwegian paintings raised awareness in Germany of that countrys scenery. He lived for a time in Brussels, then returned to Düsseldorf; in 1855 he received an honourable mention at the Paris Exposition. In 1882 he moved to Berlin, where he became a royal professor and a member of the Academy of Art; he was also a member of the Vienna, Amsterdam and Brussels Academies. He received several gold medals in Berlin and was awarded the Belgian Order of Leopold.
His son, also named August Leu (1852–76) studied under him and was a landscape and animal painter. Leu died in Seelisberg, Switzerland.