Montucla was born at Lyon.

In 1754 he published an anonymous treatise entitled Histoire des récherches sur la quadrature du cercle, and in 1758 the first part of his great work, Histoire des mathématiques, the first history of mathematics worthy of the name. He was appointed intendant - secretary of Grenoble in 1758, secretary to the expedition for colonizing Cayenne in 1764, and chief architect and censor - royal for mathematical books in 1765.

The French Revolution deprived him of his income and left him in great destitution. The offer in 1795 of a mathematical chair in one of the schools of Paris was declined on account of his infirm health, and he was still in straitened circumstances in 1798, when he published a second edition of the first part of his Histoire.

In 1778 he re-edited Jacques Ozanam's Recreations mathématiques, afterwards published in English by Charles Hutton (4 vols, London, 1803). After his death, his Histoire was completed by Jérôme Lalande, and published at Paris in 1799 - 1802 (4 vols).