Koyré was born on 29 August 1892, in the city of Taganrog, Russia, into a Jewish family. In Russia he studied in Tiflis and Odessa, before pursuing studies abroad.

In Göttingen, Germany (1908—11), he studied under Edmund Husserl and David Hilbert. Husserl did not approve of Koyré's dissertation, whereupon Koyré left for Paris, to study from 1912, notably under Henri Bergson and Léon Brunschvicg. Following Husserl's Cartesian Meditations, a series of lectures given in Paris and one of the more important of Husserl's later works, Koyré met again with Husserl repeatedly and influenced his understanding of Galileo Galilei.

In 1914 Koyré joined the French Foreign Legion as soon as the war broke out. In 1916 he volunteered for a Russian regiment fighting on the Russian front, following a cooperation agreement between the French and Russian governments.

From 1922 Koyré taught in Paris at the Ecole Pratique des Hautes Etudes (EPHE), and became a colleague of Alexandre Kojève, who eventually replaced him as lecturer on Hegel. In 1932 the EPHE created a Department of History of Religious Thought in Modern Europe for him to chair. During the years 1932—34, 1936—38, and 1940—41, Koyré taught in Fuad University (later Cairo University) where, along with André Lalande and others, he introduced the study of modern philosophy to Egyptian academia. His most important student in Cairo was Abd al-Rahman al-Badawi (1917—2002) who is considered the first systematic modern Arab philosopher. Koyré later joined the Egyptian National Committee of the Free French. He left for the United States to teach as visiting professor at the New School for Social Research in New York City. From then on his career would mostly span across EPHE and the USA (at Johns Hopkins University). His lectures at this college would form the nucleus of one of his best known publications, From the Closed World to the Infinite Universe (1957). Koyré also became a member of the Institute for Advanced Study of Princeton in 1956.

He died in Paris on 28 April 1964.

Though best known as a philosopher of science, Koyré started out as a historian of religion. Much of his originality rested on his ability to ground his studies of modern science in the history of religion and metaphysics.

Koyré focused on Galileo, Plato, and Isaac Newton. His most famous work is From the Closed World to the Infinite Universe, originally a lecture series delivered at The Johns Hopkins University in 1953, about the rise of early modern science and the change of scientists' perception of the world during the period from Nicholas of Cusa and Giordano Bruno through Newton. Though the book has been widely heralded, it was at the time more a summation of Koyré's perspective than an original new work.

Koyré was suspicious of scientists' claims to prove natural or fundamental truths through experiments. He argued that these experiments were based on complicated premises, and that they tended to prove the outlook behind these premises, rather than any real truth. He repeatedly critiqued Galileo's experiments, claiming that some of them could not have taken place, and brought into question the results that Galileo claimed and which modern historians of science had hitherto accepted.

According to Koyré, it was not the experimental or empirical nature of Galileo's and Newton's discoveries that carried the Scientific Revolution of the 16th and 17th Centuries, but a shift in perspective, a change in theoretical outlook toward the world. Koyré strongly criticized what he called the “positivist” notion that science should only discover given phenomena, the relations between them and certain laws that would help to describe or predict them. To Koyré science was, at its heart, theory: an aspiration to know the truth of the world, of uncovering the essential structures from which phenomena, and the basic laws relating to them, arise.

Koyré was also interested in the correlations between scientific discoveries and religious or philosophical world views. Not unlike Husserl in his later studies, Koyré claimed that modern science had succeeded in overcoming the split, inherent in traditional Aristotelian science, between Earth and Space, since these were now both seen as governed by the same laws. On the other hand, another split had now been created, between the phenomenal world inhabited by man and the purely abstract, mathematical world of science. Koyré aimed to show how this “first world”, the world of human dwelling (personal and historical), apparently irrelevant to modern naturalistic research, was by no means irrelevant for the very constitution and development of this research. Koyré consistently sought to show how scientific truth is always discovered in correlation with specific historical, even purely personal, circumstances.

Koyré’s work can be seen as a systematic analysis of the constitutive achievements that resulted in scientific knowledge - but with particular emphasis on the historical, and specifically human, circumstances that generate the scientists’ phenomenal world and serve as foundation for all scientific constitutions of meaning.

Koyré influenced major European and American philosophers of science, most significantly Thomas Kuhn and Paul Feyerabend. In 1961 he was awarded the Sarton Medal by the History of Science Society.