In 1830 he received his doctorate, and moved to Berlin for a year, where he continued his education under August Boeckh. In 1831 he returned to Göttingen, where in 1837 he was appointed an associate professor. From 1842 to 1883 he was a full professor of classical philology at the University of Göttingen. Following his retirement, he was replaced at Göttingen by Ulrich von Wilamowitz-Moellendorff.
Following the death of Schneidewin in 1856, Leutsch took over editorship of the Philologus, a journal on classical studies. He remained editor of the journal until his death in 1887. In 1868 he founded the philological gazette, Philologischen Anzeiger. Not a prolific author of books, Leutsch's focus was primarily on his academic teaching, with his favorite subjects being Pindar, Aristophanes, Thucydides, Livy and Tacitus.