Nicholls was born at Prevost Memorial Hospital in Donaldsonville, Louisiana, the seat of Ascension Parish, the seventh son of Thomas Clark Nicholls (himself a seventh son) and Louisa Hannah (Drake) Nicholls, a sister of the poet Joseph Rodman Drake and sister-in-law of Francis Redding Tillou. His paternal grandfather was Cornish American Edward Church Nicholls. He attended Jefferson Academy in New Orleans and graduated in 1855 from the United States Military Academy at West Point, New York. Initially assigned as a second lieutenant in the 2nd U.S. Artillery Regiment, he served in the Third Seminole War in Florida, but resigned his commission after a year and returned home.