Boissieu was born at Lyon and studied at the École Gratuite de Dessin in his hometown but was mostly self-taught.
He began making prints in the period 1758–64, then went to Italy in the retinue of the ambassador Louis Alexandre, Duc de la Rochefoucauld d'Enville (1743–1792); he met Voltaire on his way, and returned with a collection of landscape drawings.
Jean-Jacques de Boissieu realised some plates for the Diderot-d'Alembert Encyclopédie.
He continued to produce prints in Lyon, which earned him a reputation as the last representative of the older etching tradition.
His pupils included Louis Nicolas Philippe Auguste de Forbin and his nephew Claude Victor de Boissieu.