© 2018 The Author(s). An anomalous gamma-ray excess emission has been found in the Fermi Large Area Telescope data1covering the centre of the Galaxy2,3. Several theories have been proposed for this 'Galactic centre excess'. They include self-annihilation of dark-matter particles4, an unresolved population of millisecond pulsars5, an unresolved population of young pulsars6, or a series of burst events7. Here, we report on an analysis that exploits hydrodynamical modelling to register the position of interstellar gas associated with diffuse Galactic gamma-ray emission. We find evidence that the Galactic centre excess gamma rays are statistically better described by the stellar over-density in the Galactic bulge and the nuclear stellar bulge, rather than a spherical excess. Given its non-spherical nature, we argue that the Galactic centre excess is not a dark-matter phenomenon but rather associated with the stellar population of the Galactic bulge and the nuclear bulge.