David Burford, the son of Baptist minister Daniel and Elizabeth (Hawkins) Burford, was born on November 5, 1791 in North Carolina. Little is known of his early life, except that he attended only six months of school in his life and that he was apprenticed to a tanner as a young man.

The date of the Burfords' move to Tennessee is a matter of conjecture, but Rev. Daniel Burford was the first register of Smith County, Tennessee. The office of register was established in 1799. In the War of 1812, Burford served in the 7th Regiment of the US regular army as a second lieutenant, and he commanded a post at Carthage, Tennessee. From 1814 to 1815, he was acting quartermaster at Fort Pickering. After the war, he was awarded the rank of major in the state militia.

On September 16, 1825, Burford married Elizabeth W. Alexander (1808-1894), daughter of Richard and Nancy Alexander. The Burfords had at least eight children: Robert Allen, Bettie Hawkins, Jonathan, Daniel L., Mary Ann, Frances M., Clarissa, and Alice. Burford worked as a journeyman tanner and established his own tanyard in Carthage. He became associated with Robert Allen in the mercantile business and with Robert S. Chester in the tobacco trade. He eventually turned to farming and raising stock and moved to Dixon Springs, in Smith County, Tennessee, where he was to spend the rest of his life.

After establishing himself as a farmer, Burford became involved in politics and in the business of enslaving people for financial gain. As a speculator in the business of enslavement, he developed a lengthy relationship with Jourdan M. Saunders of J. M. Saunders and Co. (Warrenton, Virginia), agents for the infamous slave trading enterprise Franklin and Armfield of Alexandria, Virginia. Burford was elected sheriff of Smith County in 1825 and was re-elected in 1827. He represented Smith and Sumner Counties in the Senate of the 18th, 19th and 20th General Assemblies (1829-1835). He was elected Speaker of the Senate during the 20th General Assembly. In 1860, Burford was a delegate to the Democratic National Convention held in Charleston, South Carolina, where he supported Andrew Johnson as the party's presidential candidate. In 1861, Burford was nominated candidate to the state convention to consider secession, although the convention was never held. He died on May 23, 1864 in Dixon Springs and is buried in his family's cemetery.