Enrico Tellini was born in Castelnuovo di Garfagnana in the province of Lucca in Tuscany. After a childhood in Florence and enlistment in the Italian army he enrolled in classes at a local military college in Florence. In 1901 he was promoted to the rank of major. He participated in the Italo-Turkish War and during the First World War took part in the battle of Caporetto. 
In 1923 Tellini was part of a team of Italians sent by the League of Nations to survey the disputed border between Greece and Albania. He was shot and killed, presumably by Greek Bandits, along with three companions, when the car he was driving in was stopped by a fallen tree across the road that ran along the disputed border near the town of Yannina. Benito Mussolini demanded 50 million lira in reparations from Greece and the execution of the assassins. On August 31, 1923 Italian troops occupied Corfu in the Corfu incident.
- L'eccidio Tellini. Da Gianina all'occupazione di Corfù (agosto-settembre 1923) di Andrea Giannasi it:Andrea Giannasi, Prospettiva Editrice, 2007, ISBN 88-7418-543-X
- THE CORFU INCIDENT OF 1923: MUSSOLINI AND THE LEAGUE OF NATIONS. By James Barros. Princeton, N. J.: Princeton University Press, 1965. Pp. xxi+339