Hill was born in New York. He graduated from Rutgers University in 1859. From 1861, he worked at the Nautical Almanac Office in Cambridge, Massachusetts. His work focused on the mathematics describing the three-body problem, later the four-body problem, to calculate the orbits of the moon around earth, as well as that of planets around the sun.

Hill received a Copley Medal in 1909. He became president of the American Mathematical Society in 1894 for two years. He won the Damoiseau Prize from the Institut de France in 1898, was elected to the Royal Society of Edinburgh in 1908, as well as to the academies of Belgium (1909), Christiania (1910), Sweden (1913), among others.

Hill died in West Nyack, New York.