Aaron B. Burleson was born in Alabama on October 10, 1815, the youngest son of James and Elizabeth (Shipman) Burleson. His father was a captain under Andrew Jackson at the battles of Horseshoe Bend and New Orleans. The Burlesons returned to the old family home in Hardeman County, Tennessee, and from there, in 1827, they moved to Bastrop, Texas. Aaron was raised on the frontier and was a frequent companion of his elder brother Edward Burleson on campaigns against Indians. Aaron served under his brother's command during the siege of Bexar and saw action at the battle of San Jacinto as a member of Capt. Jesse Billingsley's Company C of Edward Burleson's First Regiment, Texan Volunteers. He was one of the party that captured Antonio López de Santa Anna.
After the Texas Revolution he lived on the upper Colorado, approximately equidistant between Bastrop and Waterloo, which became the city of Austin. His nearest neighbors on this exposed frontier were his sister Nancy Rogers, his sister and brother-in-law Rachel and James Rogers, and his brother Jacob. On February 25, 1839, Burleson, again under his eldest brother's command, took part in the battle of Brushy Creek, a decisive defeat of Comanche raiders in the upper Colorado settlements. In this fight Jacob Burleson was killed and his body badly mutilated.
In 1838 Aaron returned to Tennessee to marry Minerva J. Seaton. The couple immediately returned to Texas and settled at the mouth of Walnut Creek in Travis County. They had six children before Minerva's death in 1855. Burleson was married again, on May 15, 1856, to Jane Tannehill and with her eventually had six children.
In 1842 Burleson again served under his brother Edward, then the vice president of the Republic of Texas, in repulsing the raid of Rafael Vásquez on San Antonio. In December 1860 Governor Sam Houston commissioned Burleson to raise a company of rangers for frontier defense. Burleson amassed a considerable fortune before his death at his home near Govalle, some two miles east of Austin, on January 13, 1885. He, both of his wives, and several of his children are buried in the Rogers Hill Cemetery in Travis County.