Ampère was born in Lyons, France, where his father was a wealthy merchant. He was privately tutored, and to a large extent self-taught. His genius was evident at an early age. He was particularly proficient at mathematics and, following his marriage in 1799 he was able to make a modest living as a mathematics teacher in Lyons. In 1802 he moved first to Bourg-en-Bresse to take up an appointment, then to Paris as professor of physics and chemistry at the Ecole Centrale.

His first publication was on the statistics of games of chance Considérations sur la théorie mathématique de jeu (1802; Considerations on the Mathematical Theory of Games) and his work at Bourg led to his appointment as professor of mathematics at the Lyceum of Lyons, and then in 1809 as professor of analysis at the Ecole Polytechnique in Paris. His talents were recognized by Napoleon, who in 1808 appointed him inspector general of the newly formed university system – a post Ampère held until his death.

Ampère's most famous scientific work was in establishing a mathematical basis for electromagnetism. The Danish physicist Hans Christian Oersted had made the important experimental discovery that a current passing through a wire could cause the movement of a manetic compass needle. Ampère witnessed a demonstration of electromagnetism by François Arago at the Academy of Science on 11 September, 1820. He set to work immediately on his own investigations, and within seven days was able to report the results of his experiments.

In a succession of presentations to the academy in the next four months, he developed a mathematical theory to explain the interaction between electricity and magnetism, to which he gave the name ‘electrodynamics’ (now more commonly: electromagnetism) to distinguish it from the study of stationary electric forces, which he christened ‘electrostatics’.

Having recognized that electric currents in wires caused the motion of magnets, and that a magnet can affect another magnet, he looked for evidence that electric currents could similarly influence other electric currents. The simplest example of this interaction is found by arranging for currents to flow through two parallel wires. Ampère discovered that if the currents passed in the same direction the wires were attracted to each other, but if they passed in opposite directions the wires were repelled. From this he went on to consider more complex configurations of closed loops, helices, and other geometrical figures, and was able to provide a mathematical analysis that allowed quantitative predictions.

In 1825 he had been able to deduce an empirical law of forces (Ampère's law) between two current-carrying elements, which showed an inverse-square law (the force decreases as the square of the distance between the two elements, and is proportional to the product of the two currents). By 1827 he was able to give a precise mathematical formulation of the law, and it was in this year that his most famous work Mémoirs sur la théorie mathématique des phénomènes electrodynamiques uniquement déducte de l'expérience (Notes on the Mathematical Theory of Electrodynamic Phenomena, Solely Deduced from Experiment) was published.

Besides explaining the macroscopic effects of electromagnetism, he attempted to construct a microscopic theory that would fit the phenomenon, and postulated an electrodynamic molecule in which electric-fluid currents circulated, giving each molecule a magnetic field.

In his honor, the unit of electric current is named for him, and in fact the ampere is defined in terms of the force between two parallel current-carrying wires.