As a small child, Giorgio Santelli began taking fencing lessons from his father, the great Italian master Italo Santelli, who was one of the founders of the formidable Hungarian school of sabre fencing. By the time he was 25, Santelli had won the Austrian foil and sabre championships and the Hungarian sabre championship.

In 1924 Santelli fought a duel in Italy in defense of his father's honour. The captain of the Italian fencing team, Adolfo Cotronei, had written a story about the elder Santelli, suggesting that he had betrayed his own country by siding with a call favouring a Hungarian fencer over an Italian during a foil bout at the 1924 Olympic Games in Paris. The implication was that the old fencing master did so because he feared the Hungarian team, which he had trained, would be beaten by the Italians. Santelli stood in for his father in a duel against Cotronei with heavy cavalry sabres in an exchange that lasted for more than two minutes before Cotronei was wounded by a cut to his head.

In 1928 Santelli moved to the United States to teach at the New York Athletic Club. He quickly established himself as a successful teacher, producing many champions, including Albert Axelrod, who won third place in individual foil at the 1960 Olympic Games in Rome. Santelli also coached five strong U.S. Olympic fencing teams: 1928, 1932, 1936, 1948, and 1952.