Jesuit theologian and missionary to the New World, chiefly known for his Historia natural y moral de las Indias, the earliest survey of the New World and its relation to the Old. His works, missionary and literary, mark the end of the period of the religious and scientific incorporation of the newly discovered lands into Western culture.

Acosta joined the Jesuits in 1570, going as a missionary to Peru in 1571. Having been provincial of his order there (1576–81), he was appointed theological adviser to the Third Provincial Council of Lima (1582), later writing a catechism in local Indian languages, the first book printed in Peru. On returning to Spain in 1587, he wrote Historia natural y moral de las Indias (1590; Natural and Moral History of the Indies), which attempted to place his observations of the physical geography and natural history of Mexico and Peru (including the aboriginal religious and political institutions) in the context of contemporary Jesuit and scientific thought. Acosta's work is especially valuable as a firsthand account of western South America at this time, based on his 16 years' life and travel in the region.

Acosta led the opposition to Claudio Aquaviva (Aquaviva, Claudio) (the general of the Jesuits), helping to call the fifth Jesuit congregation to redress alleged grievances. The reformers' proposals were rejected and Acosta was imprisoned (1592–93). After submitting in 1594 Acosta became superior of the Jesuits at Valladolid and rector of the Jesuit college at Salamanca (1598), where he remained until his death.

Acosta's other significant study is the De procuranda indorum salute (1588), a systematic examination of the problems of missionary work among the newly discovered “pagans” of the New World.