The majority of the accreting supermassive black holes in the Universe are obscured by large columns of gas and dust1,2,3. The location and evolution of this obscuring material have been the subject of intense research in the past decades4,5, and are still debated. A decrease in the covering factor of the circumnuclear material with increasing accretion rates has been found by studies across the electromagnetic spectrum1,6,7,8. The origin of this trend may be driven by the increase in the inner radius of the obscuring material with incident luminosity, which arises from the sublimation of dust9; by the gravitational potential of the black hole10; by radiative feedback11,12,13,14; or by the interplay between outflows and inflows15. However, the lack of a large, unbiased and complete sample of accreting black holes, with reliable information on gas column density, luminosity and mass, has left the main physical mechanism that regulates obscuration unclear. Here we report a systematic multi-wavelength survey of hard-X-ray-selected black holes that reveals that radiative feedback on dusty gas is the main physical mechanism that regulates the distribution of the circumnuclear material. Our results imply that the bulk of the obscuring dust and gas is located within a few to tens of parsecs of the accreting supermassive black hole (within the sphere of influence of the black hole), and that it can be swept away even at low radiative output rates. The main physical driver of the differences between obscured and unobscured accreting black holes is therefore their mass-normalized accretion rate.