Snell, who was born at Leiden in the Netherlands, received his initial training in mathematics from his father, who taught at Leiden University. He traveled widely in Europe, visiting Paris, Würzburg, and Prague, and among the celebrated scientists he met were Johannes Kepler and Tycho Brahe. Once he had returned to Leiden, Snell published a number of editions of classical mathematical texts. On the death of his father (1613) Snell succeeded him as professor of mathematics at the university.

He was involved in practical work in geodesy and took part in an attempt to measure the length of the meridian. In this project he was one of the first to see the full usefulness of triangulation and published his method of measuring the Earth in his Eratosthenes Batavus (1617; The Dutch Eratosthenes). In 1621 Snell discovered his famous law of refraction, based on a constant known as the refractive index, after much practical experimental work in optics. Snell did not, however, publish his discovery and the law first reached print in Descartes's La Dioptrique (1637; Dioptrics). However, Descartes had arrived at the law in a totally different way from Snell and made no use of practical observation.