Excitons have been predicted to form spontaneously-without external excitation-in some materials. Low-temperature ARPES measurements on Ta2NiSe5 now provide evidence for such an excitonic insulator and for so-called preformed excitons. Excitons, quasiparticles of electrons and holes bound by Coulombic attraction, are created transiently by light and play an important role in optoelectronics, photovoltaics and photosynthesis. They are also predicted to form spontaneously in a small-gap semiconductor or a semimetal, leading to a Bose-Einstein condensate at low temperature, but there has not been any direct evidence of this effect so far. Here we detect the photoemission signal from spontaneously formed excitons in a debated excitonic insulator candidate, Ta2NiSe5. Our symmetry-selective angle-resolved photoemission spectroscopy reveals a characteristic excitonic feature above the transition temperature, which provides detailed properties of excitons, such as the anisotropic Bohr radius. The present result provides evidence for so-called preformed excitons and guarantees the excitonic insulator nature of Ta2NiSe5 at low temperature.