Harold Jacoby received the degree Bachelor of Arts (AB) in 1885 from Columbia College (from 1896 Columbia University), New York, and was employed there as assistant and instructor in geodesy and practical astronomy from 1888. In October 1889 he accompanied the United States scientific expedition to West Africa in USS Pensacola, under the leadership of professor D.P. Todd*. His position was that of assistant astronomer. Other members of the expedition were Cleveland Abbe* (meteorology) and E.D. Preston* (gravity and magnetic observations). The expedition arrived in Cape Town on 18 January 1890. Jacoby arranged to remain behind at the Royal Observatory, Cape of Good Hope, when the expedition left, to study the working of the heliometer under Dr David Gill*. His services as an observer and his excellent computational work were much appreciated at the observatory. He left Cape Town on 6 August 1890 to return to the United States. During his stay he had met Annie Maclear, daughter of George W.H. Maclear*, who married him in December that year.
Jacoby was appointed assistant professor of astronomy at Columbia in 1894 and that year paid a second visit to the Royal Observatory at the Cape. The next year he was awarded the degree Doctor of Philosophy (PhD). His early papers dealt mainly with the reduction of stellar observations, the determination of stellar positions and parallaxes, and instrumental errors and corrections, for example, the correction of micrometric measurements for refraction (1890), the determination of division errors of a scale (1896), the reduction of stellar photographs (1896), and, as co-author with Gill, "On the determination of the errors of the Cape reseau Gautier No. 8" (1897). He also published an analysis of Gill's observations of three minor planets, made in 1888-1889 to determine the solar parallax, in the Annals of the Cape Observatory (1896, Vol. 7). In 1902 he published his Catalogue of 287 stars near the South Pole, and optical distortion of the Cape of Good Hope astrographic telescope, followed by Photographic catalogue of 829 stars near the South Pole... (1904). His later works included Astronomy, a popular handbook (1913), Navigation (1917), and many more papers on topics in positional astronomy.
Jacoby was promoted to professor of astronomy at Columbia University in 1904, a post he held to his retirement in 1930. From 1903 he was also acting director, and from 1906 to 1930 director, of the University's astronomical observatory.