Weil studied at the Ecole Normale Supérieure in his native city of Paris and at the universities of Rome and Göttingen. He held teaching posts in many countries, including posts at the Aligarh Muslim University in India and at the universities of Strasbourg, São Paulo in Brazil, and Chicago. In 1958 he moved to the Institute for Advanced Study at Princeton, where he has been professor emeritus since 1976.

Weil's mathematical work centered on number theory, algebraic geometry, and group theory. He proved one of the central results in the theory of algebraic fields. His publications include Foundations of Algebraic Geometry (1946).

The religious philosopher and mystic Simone Weil, who died in 1943, was his sister.