Averoff was born in Metsovo, Epirus, in 1818. In 1838, he migrated to Egypt and settled in Cairo where he was employed by his brother for a few years. In 1866, he transferred all his business interests from Cairo to Alexandria. He was involved in growing and marketing cotton, a very valuable commodity at the time because of the American Civil War. Soon, he was one of richest businessmen in Egypt. He was married to Angeliki Stournaris, sister of Nikolaos Stournaris a very successful Metsovian businessman. (His sister married a Tositsa). Along with his business interests he was also philanthropist, contributing towards Greek Schools, hospitals, the army and navy. He died July 15th 1899 in Alexandria.
Averoff served as President of the Greek Community in Alexandria from 1885-1899. His niece, Michaela Averoff, a successful writer, wrote his biography .
Averoff contributed towards the completion of the Athens Polytechnic Institute, towards the purchase of a warship (purchased after his death and named after him George Averoff and towards the completion of the building of the Army Officers Academy (Greek: Σχολή των Ευελπίδων). In 1895, he contributed towards the re-marble-ing and restoration of the Panathinaiko Stadium for the 1896 Summer Olympics at the request of Crown Prince Constantine.
He also served as a member of the reception committee for the foreign competitors at the Games. In gratitude for his contributions, a statue of Averoff was commissioned and placed in front of the stadium.
- La vie impersonnelle d'Averoff. Biography of Averoff by Michaela Averoff (his niece). Translated and published in Greek 1964)