In the core of the Sun, energy is released through sequences of nuclear reactions that convert hydrogen into helium. The primary reaction is thought to be the fusion of two protons with the emission of a low-energy neutrino. These so-called pp neutrinos constitute nearly the entirety of the solar neutrino flux, vastly outnumbering those emitted in the reactions that follow. Although solar neutrinos from secondary processes have been observed, proving the nuclear origin of the Sun's energy and contributing to the discovery of neutrino oscillations, those from proton-proton fusion have hitherto eluded direct detection. Here we report spectral observations of pp neutrinos, demonstrating that about 99 per cent of the power of the Sun, 3.84 × 1033 ergs per second, is generated by the proton-proton fusion process.