Sully was born in Horncastle, Lincolnshire, England in 1783, to the actors Matthew Sully and Sarah Chester. In March 1792, the Sullys and their nine children emigrated to Charleston, South Carolina, where Thomas's uncle managed a theater. Sully made his first appearance in the theater as a tumbler at the age of 11 in Charleston. After a brief apprenticeship to an insurance broker, who recognized his artistic talent, at about age 12 Sully began painting. He studied with his brother-in-law Jean Belzons (active 1794–1812), a French miniaturist, until they had a falling-out in 1799.
He returned to Richmond to learn "miniature and device painting" from his elder brother Lawrence Sully (1769–1804). After Lawrence's death, Thomas Sully married his brother's widow, Sarah (Annis) Sully. He took on the rearing of Lawrence's children. He and Sarah had an additional nine children together. Among the children were Alfred Sully, Mary Chester Sully (who married Sully's protégé, the painter John Neagle), Jane Cooper Sully (who married a Mr. Darley), Blanche Sully, Rosalie Sully, and Thomas Wilcocks Sully.
Sully was one of the founding members of The Musical Fund Society. He painted the portraits of many of the musicians and composers who were also members.
Sully became a professional painter at age 18 in 1801. He studied portrait painting under Gilbert Stuart in Boston for three weeks. After some time in Virginia with his brother Lawrence, Sully moved to New York.
He settled in Philadelphia in 1806, where he resided for the remainder of his life. In 1809 Sully traveled to London for nine months of study under the American Benjamin West, who had established his painting career in Great Britain.
Sully died in Philadelphia on November 5, 1872. He is buried in Laurel Hill Cemetery there. His book Hints to Young Painters was published posthumously after his death.
His paintings are held and displayed permanently in many of the world's leading art museums. Two of Sully's portraits hang in the chambers of the Dialectic and Philanthropic societies of the University of North Carolina. Portraits, including that of President James K. Polk, were commissioned of notable alumni from the Societies. The obverse design of the United States Seated Liberty coinage, which began with the Gobrecht dollar in 1836 and lasted until 1891, was based on his work. The Sully painting Portrait of Anna and Harriet Coleman was sold at auction in 2013 for $145,000.