Aaron Venable Brown was born in 1795 in Brunswick County, Virginia. He studied law at the University of North Carolina, from which he graduated as valedictorian in 1814.

Brown was admitted to the Tennessee state bar in 1816 and then began to practice, becoming partners with fellow lawyer James K. Polk in 1818. In 1821, Brown was elected to the Tennessee state legislature, where he served in the state senate from 1821 to 1824, and from 1826 to 1827; he was elected to the lower house in 1831. In 1838, he was elected as a Democrat to the United States House of Representatives, where he served from 1839 to 1845. He chose not to run for reelection in 1844, instead devoting his energies to the presidential campaign of former law partner James K. Polk.

When Brown returned home to Tennessee, he discovered the Democrats had nominated him for governor. He won a close election and served one two-year term before being defeated in his reelection efforts in 1847. He was narrowly edged out as the Democratic vice-presidential candidate in 1856, but when the Democratic ticket was successful, President James Buchanan tapped Brown as his postmaster general. Aaron Venable Brown served in this capacity from 1857 until his death in 1858.