Nelson was born in Mason County, Kentucky on 20 October 1820. In 1860, he unsuccessfully ran for the United States Congress. He was appointed U.S. Envoy to Chile in 1861 by Abraham Lincoln, and to Mexico in 1869 by Ulysses S. Grant. Nelson died in Terre Haute, Indiana, on March 14, 1896, and is buried there in Woodlawn Cemetery.