He was born on 11 November 1862 as the son of the Architect Karl Koechlin and Maria Ferstel, daughter of the renowned architect Heinrich Freiherr von Ferstel. Koechlin was the brother-in-law of Aristides Brezina. Inspired by his uncle F. M. von Frieses mineral collection, Koechlin studied mineralogy, crystallography, petrography and geology at the University of Vienna and also attended lectures on mathematics, physics and chemistry. In 1887 he concluded his studies with a PhD. Since 1884, Koechlin had been a voluntary collaborator of the Imperial Mineralogical-Petrographical Department of the Natural History Museum. He not only drew up the plans for the new installation of the mineralogical collections in the new premises on the Ring, he also conducted the necessary classification work. He declined to undertake larger scientific investigations in favour of establishing a minutely detailed inventory of the fast-growing collections at that time. His listings of the diverse pieces which constituted the various collections, used only for internal purposes at the time, are still considered indispensable today when undertaking practical work in connection with the objects.
In spite of his assiduity, Koechlin was only appointed first curator in 1912. In 1920, he became Director of the Mineralogical-Petrographical Department and in 1922 he retired as privy councillor. He died in Vienna on 11 February 1939.