The path to a university education in Holland was normally through proper high schools for that purpose, but Kuiper was intent on university admission and passed an especially difficult special examination that allowed him to enter Leiden University. In the same year, he passed an examination for certification to teach high school mathematics. Kuiper's, drive, persistence, and self-assurance, already well developed in his student days, moved him to succeed in spite of an atmosphere of discrimination at Leiden against poorer students and those who had not studied in the proper high schools.

At a young age, Kuiper's interest in astronomy was sparked when he read the philosophical and cosmological writings of Descartes. This interest was encouraged by his father and his grandfather, who gave him a small telescope. With his naked eye, Kuiper made sketches throughout an entire winter to record the faintest members of the Pleiades star cluster that he could detect. On his master chart, Leiden Observatory astronomers, to whom he sent the results, found the limiting magnitude 7.5, nearly four times fainter than those visible to the normal human eye. Even in his later years, Kuiper's visual acuity was exceptional.

Kuiper entered Leiden University in September 1924. His fellow student and long-time friend Bart J. Bok recalled the day they met as incoming students in the library of the Institute of Theoretical Physics. Kuiper explained to Bok that he intended to pursue astronomical problems of a fundamental nature, specifically the three-body problem and related questions about the nature and origin of the solar system. He completed a B.Sc. at Leiden in 1927 and immediately went on to postgraduate studies. Among Kuiper's professors at Leiden were Ejnar Hertzsprung, Antonie Pannekoek, and the theoretical physicist Paul Ehrenfest.