Harris was born in Plymouth and studied at the University of Edinburgh. In 1820 he invented a new method of arranging the lightning conductors of ships, the peculiarity of which was that the metal was permanently fixed in the masts and extended throughout the hull; but it was only with great difficulty, and not till nearly thirty years afterwards, that his invention was adopted by the government for the Royal Navy.
In 1835 he received the Copley Medal from the Royal Society for his papers on the laws of electricity of high tension, and in 1847 he was knighted.