Born in Cooperstown, New York, Nelson graduated from Yale College in 1846, where he was a member of Skull and Bones,:71 and read law to enter the bar in 1849. He was in private practice in Buffalo, New York from 1849 to 1850, and then in St. Paul, Minnesota Territory until 1853. He was a county attorney of Douglas County, Wisconsin from 1853 to 1855, returning to private practice in St. Paul until 1857. He was an associate justice of the Minnesota Territorial Supreme Court from 1857 to 1858.
On May 20, 1858, Nelson was nominated by President James Buchanan to a new seat on the United States District Court for the District of Minnesota created by 11 Stat. 285. He was confirmed by the United States Senate on May 30, 1858, and received his commission on May 20, 1858. Nelson served in that capacity until his retirement from the bench, on May 16, 1896.
He then returned to his private practice in St. Paul, Minnesota, until his death in that city in 1904.
- Rensselaer Nelson at the Biographical Directory of Federal Judges, a public domain publication of the Federal Judicial Center.
- "The twelfth general catalogue of the Psi Upsilon Fraternity". 1917. Retrieved March 24, 2011.