He was the son of William Richard Hamilton (1777-1859), and was educated at Charterhouse and the University of Göttingen. He became a fellow of the Geological Society of London in 1831. In 1835 he made a geological tour of the Levant with Hugh Edwin Strickland, continuing on his own through Armenia and across Asia Minor. This journey was described in Researches in Asia Minor, Pontus, and Armenia (1842).
Hamilton was president of the Geological Society between 1854 and 1866. He was MP for Newport, Isle of Wight from 1841 to 1847. He made excursions in France and Belgium and wrote on the rocks and minerals of Tuscany, the agate quarries of Oberstein, and on the geology of the Mayence basin and the Hesse-Cassel district.