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Galileo's drawings show that he first observed Neptune on 27 December 1612, and again on 27 January 1613. On both occasions, Galileo mistook Neptune for a fixed star when it appeared very close—in conjunction—to Jupiter in the night sky; hence, he is not credited with Neptune's discovery. During the period of his first observation in December 1612, Neptune was stationary in the sky because it had just turned retrograde that very day. This apparent backward motion is created when the orbit of the Earth takes it past an outer planet. Since Neptune was only beginning its yearly retrograde cycle, the motion of the planet was far too slight to be detected with Galileo's small telescope. In July 2009, University of Melbourne physicist David Jamieson announced new evidence suggesting that Galileo was at least aware that the star he had observed had moved relative to the fixed stars.

In 1821, Alexis Bouvard published astronomical tables of the orbit of Neptune's neighbour Uranus. Subsequent observations revealed substantial deviations from the tables, leading Bouvard to hypothesize that an unknown body was perturbing the orbit through gravitational interaction. In 1843, John Couch Adams began work on the orbit of Uranus using the data he had. Via Cambridge Observatory director James Challis, he requested extra data from Sir George Airy, the Astronomer Royal, who supplied it in February 1844. Adams continued to work in 1845–46 and produced several different estimates of a new planet.

In 1845–46, Urbain Le Verrier, independently of Adams, developed his own calculations but also experienced difficulties in stimulating any enthusiasm in his compatriots. In June 1846, upon seeing Le Verrier's first published estimate of the planet's longitude and its similarity to Adams's estimate, Airy persuaded Challis to search for the planet. Challis vainly scoured the sky throughout August and September.

Meantime, Le Verrier by letter urged Berlin Observatory astronomer Johann Gottfried Galle to search with the observatory's refractor. Heinrich d'Arrest, a student at the observatory, suggested to Galle that they could compare a recently drawn chart of the sky in the region of Le Verrier's predicted location with the current sky to seek the displacement characteristic of a planet, as opposed to a fixed star. The very evening of the day of receipt of Le Verrier's letter on 23 September 1846, Neptune was discovered within 1° of where Le Verrier had predicted it to be, and about 12° from Adams' prediction. Challis later realised that he had observed the planet twice in August (Neptune had been observed on 8 and 12 August, but because Challis lacked an up-to-date star-map it was not recognised as a planet), failing to identify it owing to his casual approach to the work.

In the wake of the discovery, there was much nationalistic rivalry between the French and the British over who had priority and deserved credit for the discovery. Eventually an international consensus emerged that both Le Verrier and Adams jointly deserved credit. Since 1966 Dennis Rawlins has questioned the credibility of Adams's claim to co-discovery and the issue was re-evaluated by historians with the return in 1998 of the "Neptune papers" (historical documents) to the Royal Observatory, Greenwich. After reviewing the documents, they suggest that "Adams does not deserve equal credit with Le Verrier for the discovery of Neptune. That credit belongs only to the person who succeeded both in predicting the planet's place and in convincing astronomers to search for it."