He studied at the Collegio dei nobili in Parma and then enlisted in the Guardia Real in Spain and served in the Spanish Navy.
He fled from the Spanish Inquisition, and was in Paris in 1783 where he observed the first unmanned balloon flights by the Montgolfier brothers.
He then moved to London and launched the first unmanned balloon in Britain on 4 November 1783, a year before the first manned flight in England by Vincent Lunardi, releasing a 5 feet (1.5 m) hydrogen balloon from the house of Michael Biaggini, a maker of artificial flowers made from silk and other fabrics, at 33 Noble Street, on Cheapside.
Zambeccari was commissioned to launch a balloon in Venice in April 1784, an occasion that was painted by Francesco Guardi.
Zambeccari and Admiral Sir Edward Vernon ascended in a 34 feet (10 m) balloon from Tottenham Court Road on 23 March 1785 and landed later the same day near Horsham.
His remains were moved to the Certosa di Bologna in 1813, but returned to San Francesco in 1926 to be interred with his son Livio in the monument to his relation Alessandro Zambeccari.