The son of the watercolourist Alexander Cozens, John began to exhibit drawings with the Society of Artists in 1767. The two long visits he paid to the Continent, 1776–79 and 1782–83, were the formative and decisive events in his career. On the first occasion he travelled through Switzerland to Italy, and spent much time in Rome. His second visit was made with the author William Beckford, who had studied drawing under Alexander Cozens, and whom he accompanied as far as Naples. Cozens became insane in 1793 and spent the remainder of his life under the care of Thomas Monro, an alienist and amateur draftsman.

Cozens found the subject matter of his art in the Alps and the Roman Campagna. Painting in low-toned combinations of blue, green, and gray watercolour, he evoked a haunting and sometimes melancholy poetry. Thomas Girtin and J.M.W. Turner copied his works in their early years, and first learned from him the full range of watercolour as an expressive medium.