Born in Dresden, Saxony, Elliot joined the Royal Navy in 1815 and served as a midshipman in the bombardment of Algiers against Barbary pirates the following year. After serving in the East Indies Station for four years, he joined the Home Station in 1820. He joined the West Africa Squadron and became a lieutenant in 1822. After serving in the West Indies Station, he was promoted to captain in 1828. He met Clara Windsor in Haiti and they married in 1828.