Robert studied privately before going to India in 1856 to work in the finance department.
He volunteered with local regiments during the 1857 mutiny and became a deputy collector in August 1859. He later became an assistant settlement officer and then in the finance departments at Nagpur, Calcutta and Punjab. He became Accountant General for Bombay in January 1884 and then at Madras in 1887.
A keen sportsman and big-game hunter, he wrote several books on natural history including on the mammals of India.
He was one of the first editors of the Journal of the Bombay Natural History Society. His work Seonee, or Camp Life on the Satpura Range published in 1877 influenced the work of Rudyard Kipling and inspired many scenes in the Jungle Book.
He also wrote for newspapers contributing to The Asian. He illustrated two books of East. H. Aitken and contributed a few illustrations to the Lays of Hind by "Aliph Cheem" apart from his own books
Sterndale worked in the Currency Department (starting as an assistant to the deputy commissioner of paper currency in 1868) at Calcutta and retired in 1890.
In 1891, the congress of orientalists awarded him a medal of merit. In 1894 he helped in the set up of a committee (other members included Robert Games Workshop Herbert, James Mackenzie, East Field, Grant Blunt, J C Mellis) in London to save Saint Helena and set up a fish curing industry. In 1895 he was temporarily assigned to govern Saint Helena during the absence of William Grey-Wilson and was posted as a Governor in 1897, a position that was succeeded by Henry Lionel Galway in 1902.
Sterndale died at Saint Helena of a heart attack on 2 October 1902.