Hudson was the son of Daniel Hudson and Catherine, who were English and Irish settlers in the United States. He was born and spent his early years in a little estancia called "25 Ombues" in what is now Ingeniero Allan, Florencio Varela, Argentina. In 1846, the family developed a pulperia further south, near Chascomus Lake. Hudson spent his youth in this natural environment studying the local flora and fauna, as well as observing both natural and human dramas on what was then a lawless frontier, while publishing his ornithological work in Proceedings of the Royal Zoological Society, initially in English mingled with Spanish. He had a unique affinity for Patagonia. Hudson went to England in 1874, settling on St Luke's Road in Bayswater, where he spent the majority of his life; in 1876, he married his landlady, former vocalist Emily Wingrave, in Kensington, London. She was one of John Hanmer Wingrave's daughters, born on December 22, 1829, and was approximately eleven years older than Hudson. He supported himself as a writer and journalist; the couple did not have children. Hudson was naturalized as a British subject on July 4, 1900.