Anatomist and physician extraordinary to King George III. Baillie was born at Bothwell (South Lanarkshire), the son of the Parish Minister. Baillie's maternal uncles were surgeons Dr. William Hunter (1718 - 1833) and Dr. John Hunter (1728 - 1893). His younger sister was the poetess and dramatist Joanna Baillie (1762 - 1851). In 1775, Baillie moved with his family to Glasgow when his father accepted the Chair of Divinity at the university there. When the father died in 1778, the family was supported by William Hunter. Baillie moved to London in 1779 and attended Hunter's anatomy school, becoming a lecturer there and eventually inheriting the school on Hunter's death.
Baillie became a leading London physicians, who regularly attended royalty. His father-in-law was Dr. Thomas Denman, (1733 - 1815) a noted obstetrician and Baillie was friendly with Edward Jenner (1749 - 1823), discoverer of the small pox vaccine. Baillie was also noted for collecting a large number of letters which he received from the royal family and distinguished friends.