Angelo received his initial training in the Italian method of fencing in Pisa. After moving to Paris, he studied the classic French style with the foil at the Royal Association of Masters of Yielding Weapons of the City and Suburbs of Paris under the tutelage of Teillagory, who also trained Charles, chevalier d'Éon de Beaumont (Éon de Beaumont, Charles, chevalier d'), the famous French spy.

In the early 1750s Angelo became infatuated with the celebrated Irish actress Margaret (“Peg”) Woffington, who was on tour in Paris, and accompanied her back to London, where he quickly established his reputation as an expert fencer. He soon opened Angelo's School of Arms in Soho, and by 1758 he was instructing members of the royal family, including the prince of Wales (later King George III) and his brother, Prince Edward Augustus. His school was also famous for accepting female students, some of whom were actresses from London theatres who first accompanied their male colleagues and then decided to take lessons. In 1760 Angelo turned the school over to one of his sons and took a position at Eton College. Angelo's descendants were still operating the school during the latter half of the 19th century.

Angelo's teaching methods, if not particularly original, were sound and methodical, employing a combination of actions useful for both practice and dueling. Angelo's classic treatise, L'École des armes (1763; The School of Fencing), included colourful instructional sketches by London's most accomplished illustrators; some historians have suggested that the chevalier d'Éon de Beaumont, who had joined Angelo in London, may have assisted with the French text. This work and its illustrations were considered so excellent that when Denis Diderot (Diderot, Denis) and Jean Le Rond d' Alembert (Alembert, Jean Le Rond d') were compiling their Encyclopédie, they obtained Angelo's permission to use the full treatise and its illustrations for the encyclopaedia's fencing entry. It should be noted that much of the fencing depicted by Angelo resembles, in form, fencing as it is practiced today.