Nelson was born in Minerva, Mason County, Kentucky to Dr. Thomas W. Nelson and Frances Doniphan Nelson. In 1844, Thomas married Elizabeth "Lizzie" Key, the daughter of Marshall Key and Harriet Sellman Key. She was a student of Harriet Beecher Stowe.
The Nelsons moved to Rockville, Indiana, where he set up a law practice. A few years later, the couple moved to Terre Haute, Indiana. In 1852 he was on the Board of Commissioners for the construction of the Springfield and Terre Haute Railroad. During the 1850s, he was tasked with organizing the Republican Party in Indiana. In 1860, he unsuccessfully ran for the United States Congress. He was appointed U.S. Envoy to Chile in 1861 by Abraham Lincoln. On December 8, 1863, he organized rescue operations during the catastrophic Church of the Company Fire in Santiago and was called "a true hero of Chile" for doing so.
| United States Envoy to Chile
4 October 1861 – 12 March 1866
Hugh Judson Kilpatrick
William S. Rosecrans
| United States Envoy to Mexico
June 26, 1869 – June 16, 1873
John W. Foster
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