William Waller Carson was born in Mississippi on June 2, 1845, to Dr. James Greene and Catherine Waller Carson. He was raised primarily in Louisiana. In 1863, he enlisted in the 4th Louisiana Cavalry Regiment (CSA), where he served until 1865. After the war, he resumed his education and graduated from Washington College (later Washington and Lee University) with his Civil Engineering (C. E.) degree in 1868 and his Mining Engineering (M. E.) degree in 1869. After graduation, he worked on several civil engineering projects before becoming a professor of mathematics at Davidson College (North Carolina) in 1877. He held this post until 1883. He married Rachel Finnie of Memphis, Tennessee, in December of 1880, and they had three children. In 1885, he became a professor of civil engineering at the University of Tennessee. For many years, Uncle Billy (as his students called him) constituted the University's entire Civil Engineering Department. He retired from this post in 1916.

Carson was also extremely active in Confederate veterans' affairs, and was the commander of the Fred Ault Camp, No. 5, of the United Confederate Veterans from 1912 until his death. Carson died in Knoxville on February 7, 1930.