At his native town of Clazomenae in Asia Minor, he appears to have had some amount of property and prospects of political influence; he supposedly surrendered both of these out of a fear that they would hinder his search for knowledge. Although a Greek, he was probably a Persian citizen, perhaps even a soldier of the Persian army since Clazomenae was suppressed during the Ionian Revolt.

In early manhood (c. 464-462 BCE) he went to Athens, which was rapidly becoming the centre of Greek culture. There he is said to have remained for thirty years. Pericles learned to love and admire him, and the poet Euripides derived from him an enthusiasm for science and humanity. Some authorities assert that even Socrates was among his disciples.

Anaxagoras brought philosophy and the spirit of scientific inquiry from Ionia to Athens. His observations of the celestial bodies led him to form new theories of the universal order; he attempted to give a scientific account of eclipses, meteors, rainbows and the sun, which he described as a mass of blazing metal, larger than the Peloponnesus. The heavenly bodies, he asserted, were masses of stone torn from the earth and ignited by rapid rotation. However, these theories brought him into collision with the popular faith.

Anaxagoras was arrested by his friend Pericles' political opponents on a charge of contravening the established dogmas of religion (some say the charge was one of Medism), and it required all the eloquence of Pericles to secure his release. Even so he was forced to retire from Athens to Lampsacus in Ionia (434-433 BCE), where he died about 428 BCE. Citizens of Lampsacus erected an altar to Mind and Truth in his memory, and observed the anniversary of his death for many years afterward.

Anaxagoras wrote a book of philosophy, but only fragments of the first part of this have survived through the preservation of Simplicius of Cilicia (6th century CE).