Bradley was born at Sherborne, near Cheltenham in Gloucestershire, to William Bradley and Jane Pound in September 1692. His brother John was also an astronomer. After attending Westwood's Grammar School at Northleach in Gloucestershire, he entered Balliol College, Oxford, on 15 March 1711, and took degrees of Bachelor of Arts and Master of Arts in 1714 and 1717 respectively. His early observations were made at the rectory of Wanstead in Essex, under the tutelage of James Pound, his uncle and a skilled astronomer. Bradley was elected a fellow of the Royal Society on 6 November 1718.