Simon Newcomb was born in the town of Wallace, Nova Scotia. His parents were Emily Prince, the daughter of a New Brunswick magistrate, and itinerant school teacher John Burton Newcomb. John moved around teaching in different parts of Canada, particularly in different villages in Nova Scotia and Prince Edward Island. Newcomb seems to have had little conventional schooling other than from his father and from a short apprenticeship to Dr. Foshay, a charlatan herbalist, in New Brunswick in 1851. Nevertheless, his father provided him with an excellent foundation for his future studies. Newcomb's apprenticeship with Dr. Foshay occurred when he was only 16. They entered an agreement that Newcomb would serve a five-year apprenticeship during which time Foshay would train him in using herbs to treat illnesses. For two years he was an apprentice but became increasingly unhappy and disillusioned with his apprenticeship and about Foshay's unscientific approach, realizing that the man was a charlatan. He made the decision to walk out on Foshay and break their agreement. He walked the 120 miles to the port of Calais in Maine where he met the captain of a ship who agreed to take him to Salem, Massachusetts, so that he could join his father. In about 1854, he joined his father in Salem (John Newcomb had moved earlier to the United States), and the two journeyed together to Maryland.

After arriving in Maryland, Newcomb taught for two years from 1854 to 1856; for the first year in a country school in Massey's Cross Roads, Kent County, then for a year at a school not far south in Sudlersville. In his spare time he studied a variety of subjects such as political economy and religion, but his deepest studies were made in mathematics and astronomy. In particular he read Newton's Principia at this time. In 1856 he took up a position as a private tutor close to Washington and he often travelled to that city to study mathematics in the libraries there. He was able to borrow a copy of Bowditch's translation of Laplace's Traité de mécanique céleste from the library of the Smithsonian Institution but found that the mathematics which the book contained was rather beyond his current knowledge.

Newcomb studied mathematics and physics privately and supported himself with some school teaching before becoming a human computer (a functionary in charge of calculations) at the Nautical Almanac Office in Cambridge, Massachusetts, in 1857. At around the same time, he enrolled at the Lawrence Scientific School of Harvard University, graduating BS in 1858. Newcomb studied mathematics under Benjamin Peirce and the impecunious Newcomb was often a welcome guest at the Peirce home. However, he later became envious of Peirce's talented son, Charles Sanders Peirce and has been accused of a "successful destruction" of C.S. Peirce's career. In particular, Daniel Coit Gilman, president of Johns Hopkins University, is alleged to have been on the point of awarding tenure to C.S. Peirce, before Newcomb intervened behind the scenes to dissuade him. About 20 years later, Newcomb allegedly influenced the Carnegie Institution Trustees, to prevent C.S. Peirce's last chance to publish his life's work, through a denial of a Carnegie grant to Peirce, even though Andrew Carnegie himself, Theodore Roosevelt, William James and others, wrote to support it.

In the prelude to the American Civil War, many US Navy staff of Confederate sympathies left the service and, in 1861, Newcomb took advantage of one of the ensuing vacancies to become professor of mathematics and astronomer at the United States Naval Observatory, Washington D.C.. Newcomb set to work on the measurement of the position of the planets as an aid to navigation, becoming increasingly interested in theories of planetary motion.

By the time Newcomb visited Paris, France, in 1870, he was already aware that the table of lunar positions calculated by Peter Andreas Hansen was in error. While in Paris, he realised that, in addition to the data from 1750 to 1838 that Hansen had used, there was further data stretching as far back as 1672. His visit allowed little serenity for analysis as he witnessed the defeat of French emperor Napoleon III in the Franco - Prussian War and the coup that ended the Second French Empire. Newcomb managed to escape from the city during the ensuing rioting that led up to the formation of the Paris Commune and which engulfed the Paris Observatory. Newcomb was able to use the "new" data to revise Hansen's tables.

He was offered the post of director of the Harvard College Observatory in 1875 but declined, having by now settled that his interests lay in mathematics rather than observation.

In 1877 he became director of the Nautical Almanac Office where, ably assisted by George William Hill, he embarked on a program of recalculation of all the major astronomical constants. Despite fulfilling a further demanding role as professor of mathematics and astronomy at Johns Hopkins University from 1884, he conceived with A.M.W. Downing a plan to resolve much international confusion on the subject. By the time he attended a standardisation conference in Paris, France, in May 1896, the international consensus was that all ephemerides should be based on Newcomb's calculations. A further conference as late as 1950 confirmed Newcomb's constants as the international standard.

In 1878, Newcomb had started planning for a new and precise measurement of the speed of light that was needed to account for exact values of many astronomical constants. He had already started developing a refinement of the method of Léon Foucault when he received a letter from the young naval officer and physicist Albert Abraham Michelson who was also planning such a measurement. Thus began a long collaboration and friendship. In 1880, Michelson assisted at Newcomb's initial measurement with instruments located at Fort Myer and the United States Naval Observatory, then situated on the Potomac River. However, Michelson had left to start his own project by the time of the second set of measurements between the observatory and the Washington Monument. Though Michelson published his first measurement in 1880, Newcomb's measurement was substantially different. In 1883, Michelson revised his measurement to a value closer to Newcomb's.

In 1881, Newcomb discovered the statistical principle now known as Benford's law, when he observed that the earlier pages of logarithm books, used at that time to carry out logarithmic calculations, were far more worn than the later pages. This led him to formulate the principle that, in any list of numbers taken from an arbitrary set of data, more numbers will tend to have the leading digit "1" than any other leading digit.

In 1891, within months of Seth Carlo Chandler’s discovery of the 14 month variation of latitude, now referred to as the Chandler wobble, Newcomb explained the apparent conflict between the observed motion and predicted period of the wobble. The theory was based on a perfectly rigid body, but Earth is slightly elastic. Newcomb used the variation of latitude observations to estimate the elasticity of Earth, finding it to be slightly more rigid than steel.

Newcomb was an autodidact and polymath. He wrote on economics and his Principles of political economy (1885) was described by John Maynard Keynes as "one of those original works which a fresh scientific mind, not perverted by having read too much of the orthodox stuff, is able to produce from time to time in a half-formed subject like economics." He was credited by Irving Fisher with the first-known enunciation of the equation of exchange between money and goods used in the quantity theory of money. He spoke French, German, Italian and Swedish; was an active mountaineer; widely read; and authored a number of popular science books and a science fiction novel, His Wisdom the Defender (1900).

Newcomb died in Washington, DC of bladder cancer and was buried with military honors in Arlington National Cemetery with President William Howard Taft in attendance.

Newcomb's daughter married Assistant US Attorney General Edward Baldwin Whitney, who was the son of Professor William Dwight Whitney and the grandson of US Senator & Connecticut Governor Roger Sherman Baldwin. He was also the grandfather of famed mathematician and Professor Hassler Whitney.