He studied at Leipzig, taught at the Saalfeld Progymnasium (1837) and at the Dresden Kreuzschule (1840).
In February 1849, Köchly was elected to the lower house of the Kingdom of Saxony, but that same year was forced to flee to Brussels on account of his participation in the May insurrection.
He was appointed professor of classical philology at Zürich in 1851, and at Heidelberg in 1864.
The scheme set forth in these pamphlets stressed the natural sciences, and, in Latin and Greek, urged emphasis on content rather than on grammar and style, and the gradual abolition of speaking and writing those languages.
A collection of his smaller works is found in his Opuscula academica (Leipzig, 1853–56), Akademische Vorträge und Reden (Zürich, 1856) and Opuscula philologica (Leipzig 1881–82).