Nicholson was the son of a farmer from Springfield, Illinois. He graduated from Drake University, Des Moines, Iowa, in 1912 and in 1915 obtained his PhD from the University of California. From then until his retirement in 1957 he worked at the Mount Wilson Observatory, California.

While still a graduate student at the Lick Observatory, Nicholson discovered the ninth satellite of Jupiter (Sinope) in 1914, working close to the limits of resolution of the Lick telescope and the photographic plates then available. He went on to discover a further three satellites, Jupiter X (Lysithea) and XI (Carme) in 1938 and Jupiter XII (Ananke) in 1951. All four satellites are very small, about 15–20 kilometers (9–12 mi) in diameter.

Nicholson studied the surface features and spectrum of the Sun and also, in collaboration with Edison Petit, worked on planetary and lunar temperatures. Thus they showed in 1927 that the Moon undergoes enormous temperature changes, for in the course of an eclipse its surface temperature dropped from 160°F to –110°F (71°C to –79°C) in about an hour.