He was born in Bedano in the province of Ticino. He was the nephew of Giocondo Albertolli, a professor of architecture at the Brera Academy. In 1797, Giacomo became professor of civil architecture in the Seminary of Padua. With the Austrian occupation, he moved to Milan, where he replaced his teacher, Giuseppe Piermarini. He died of apoplexy (stroke).
- Rambelli, Gianfrancesco (1834). Emilio de Tipaldo (ed.). Biografia degli Italiani illustri nelle scienze: lettere ed arti del Secolo XVIII, e de'Contermporanei. Tipografia di Alvisopoli, Venice. pp. 251–252.