His father was the Business partner of his maternal grandfather in lace Manufacturing, a traditional industry in Calais. Debreu was orphaned at an early age, as his father committed suicide and his mother died of natural causes. Prior to the start of World War II, he received his baccalauréat and went to Ambert to begin preparing for the entrance examination of a grande école. Later on, he moved from Ambert to Grenoble to complete his preparation, both places being in Vichy France during World War II. In 1941, he was admitted to the École Normale Supérieure in Paris, along with Marcel Boiteux (fr). He was influenced by Henri Cartan and the Bourbaki Writers. When he was about to take the final examinations in 1944, the Normandy landings occurred and he, instead, enlisted in the French army. He was transferred for training to Algeria and then served in the occupying French forces in Germany until July 1945. Debreu passed the Agrégation de Mathématiques exams at the end of 1945 and the beginning of 1946. By this time, he had become interested in economics, particularly in the general equilibrium theory of Léon Walras. From 1946 to 1948, he was an assistant in the Centre National de la Recherche Scientifique. During these two and a half years, he made the transition from mathematics to economics. In 1948, Debreu went to the United States on a Rockefeller Fellowship which allowed him to visit several American universities, as well as those in Uppsala and Oslo in 1949–50.

Debreu married Françoise Bled in 1946 and they had two daughters, Chantal and Florence, born in 1946 and 1950 respectively.

Debreu began working as a Research Associate and joined the Cowles Commission at the University of Chicago in the summer of 1950. He remained there for five years, returning to Paris periodically.

In 1954, he published a breakthrough paper, entitled Existence of an Equilibrium for a Competitive Economy, together with Kenneth Arrow, in which they provided a definitive mathematical proof of the existence of a general equilibrium, using topological rather than calculus-based methods.

In 1959, he published his classical monograph, Theory of Value: An Axiomatic Analysis of Economic Equilibrium (Cowles Foundation Monographs Series), which is one of the most important works in mathematical economics. He also studied several problems in the theory of cardinal utility, in particular the additive decomposition of a utility function defined on a Cartesian product of sets.

During his sabbaticals in the late 1960s and 1970s, he visited universities in Leiden, Cambridge, Bonn and Paris.

In January 1962, he started working at the University of California, Berkeley, where he held the titles of University Professor and Class of 1958 Professor of Economics and Mathematics Emeritus.

In 1976, he received the French Legion of Honour. He was awarded the 1983 Bank of Sweden Prize in Economic Sciences in Memory of Alfred Nobel, for having incorporated new analytical methods into economic theory and for his rigorous reformulation of general equilibrium theory. He was a member of the International Academy of Science.

In 1990, he served as President of the American Economic Association.

Debreu died in Paris at the age of 83 of natural causes on New Year's Eve, 2004.

His later studies centred mainly on the theory of differentiable economies, where he showed that, in general, aggregate excess demand functions vanish at a finite number of points – basically, he showed that economies have a finite number of price equilibria.