The son of an itinerant teacher, Newcomb was born at Wallace in Nova Scotia and had little formal education. He was apprenticed to a herbalist in Nova Scotia but ran away to join his father in the United States. In 1857 he joined the American Nautical Almanac Office, and he graduated from Harvard in 1858. He joined the corps of professors of mathematics in the navy, and became professor of mathematics at the Naval Observatory in Washington in 1861. From 1884 to 1894 he was professor of mathematics and astronomy at Johns Hopkins University. He was also superintendent of the American Nautical Almanac from 1877 to 1897, retiring with the rank of rear admiral. In addition he was the editor of the American Journal of Mathematics and the author of over 350 scientific papers and a number of popular works on astronomy.

Newcomb worked for many years on new tables for the planets and the Moon, which were published in 1899. These, together with his organization of the Nautical Almanac, were his major astronomical work. His tables, the result of detailed observations and sophisticated mathematics, were the most accurate ever made and were in constant use until the middle of this century. Also of major importance was his production and promotion of a new, unified, and more accurate system of astronomical constants, which was adopted worldwide in 1896.

He did much to encourage younger scientists. Hearing the young Albert Michelson lecture to the American Association for the Advancement of Science on new methods for accurately determining the speed of light, he went out of his way to raise money for the unknown young scientist to continue with his work.