Hudson was born in the borough of Quilmes, now Florencio Varela of the greater Buenos Aires, in Buenos Aires Province, Argentina. He was the son of Daniel Hudson and his wife Catherine née Kemble, U.S. settlers of English and Irish origin. He spent his youth studying the local flora and fauna and observing both natural and human dramas on what was then a lawless frontier, publishing his ornithological work in Proceedings of the Royal Zoological Society, initially in an English mingled with Spanish idioms. He had a special love of Patagonia.