Nicholson was born in Springfield, Illinois and was raised in rural Illinois; he was educated at Drake University where he became interested in astronomy.
In 1914, at the University of California's Lick Observatory, while observing the recently-discovered Jupiter moon Pasiphae, he discovered a new one: Sinope, which he computed its orbit for his PhD thesis in 1915.
He spent his entire career at Mount Wilson Observatory, where he discovered three more Jovian moons: Lysithea and Carme in 1938 and Ananke in 1951, as well as a Trojan asteroid, and computed orbits of several comets and of Pluto.
At Mt. Wilson, his main assignement concerned solar activity and he produced for decades annual reports on sunspot activity. He also made a number of eclipse expeditions to measure the brightness and temperature of the Sun's corona.
In the early 1920s, he and Edison Pettit made the first systematic infrared observations of celestial objects. They used a vacuum thermocouple to measure the infrared radiation and thus the temperature of the moon which led to the theory that the moon was covered with a thin layer of dust acting as an insulator, and also of the planets, sunspots and stars. Their temperatures measurements of nearby giant starss led to some of the first determinations of stellar diameters.
From 1943 to 1955, he served as editor of the Publications of the Astronomical Society of the Pacific, of which he was also twice president. In 1963 was awarded by the Bruce Medal and died shortly after in Los Angeles.