He one of the twin elder sons of Robert Penny, surgeon, by Clare, daughter of William Trafford, of
Swythamley, Staffordshire, and was born at Knutsford, Cheshire in 1714. He was sent to London and placed under the tuition of Thomas Hudson; later he went to Rome and studied under
Marco Benefiale. He returned to England about 1748, and began his professional career by painting small whole-lengths; later he painted more demanding subjects.
Penny appears to have joined the Incorporated Society of Artists in 1762; but with Benjamin West, Richard Wilson, and others, then withdrew because of internal frictions. In December 1768 he was nominated one of the foundation members of the Royal Academy of Arts, and its first professor of painting. He then ceased to exhibit, and was obliged by ill-health to resign the professorship of painting, in which he was succeeded by James Barry.
Penny died at Chiswick on 16 November 1791, and was buried with his wife at Chessington, Surrey.