Born at Maastricht in the Netherlands, Debye studied electrical engineering at Aachen and gained his PhD at Munich in 1910. He held chairs of physics at Zurich (1911–12 and 1919–27), Utrecht (1912–14), Göttingen (1914–19), and Leipzig. He was director of the Kaiser Wilhelm Institute for Theoretical Physics (1935–40) before emigrating to America where he was professor of chemistry at Cornell (1940–50).

Debye was essentially a theoretician and most of his work, although varied, had a common theme: the application of physical methods to problems of molecular structure. An early work was the derivation of a relation governing the change of the specific heat capacity of solids with temperature. In 1915 he gave a theoretical treatment of electron diffraction by gases, not realized in practice until 1930. At Göttingen, Debye and P. Scherrer discovered a method of producing x-ray diffraction patterns from powders. This was later extended to the production of diffraction patterns from simple molecules such as tetrachloromethane, CCl₄ (1928).

A major part of Debye's work was devoted to dipole moments, beginning in 1912. He used these to determine the degree of polarity of covalent bonds and to determine bond angles. Together with his x-ray work and results from rotational spectra, this enabled the precise spatial configuration of small molecules to be deduced. For example, the planarity of the benzene molecule was confirmed by dipole moment measurements. It was for his work on dipole moments and for work on the diffraction of x-rays and electrons in gases that Debye was awarded the 1936 Nobel Prize for chemistry. Debye is probably better known, however, for the Debye–Hückel theory of electrolytes (1923). This was a theory that could be applied to concentrated solutions of ionic compounds, and was a great advance on the theories of the time, which applied only to very dilute solutions. The Debye–Hückel theory takes account of the fact that an ion in solution tends to attract other ions of opposite charge.