We present a new global fit of the 19-dimensional phenomenological Minimal Supersymmetric Standard Model (pMSSM-19) that comply with all the latest experimental results from dark matter indirect, direct and accelerator dark matter searches. We show that the model provides a satisfactory explanation of the excess of gamma-rays from the Galactic centre observed by the Fermi~Large Area Telescope, assuming that it is produced by the annihilation of neutralinos in the Milky Way halo. We identify two regions that pass all the constraints: the first corresponds to neutralinos with a mass ~80-100 GeV annihilating into WW with a branching ratio of 95% ; the second to heavier neutralinos, with mass ~180-200 GeV annihilating into t tbar with a branching ratio of 87%. We show that neutralinos compatible with the Galactic centre GeV excess will soon be within the reach of LHC run-II -- notably through searches for charginos and neutralinos, squarks and light smuons -- and of Xenon1T, thanks to its unprecedented sensitivity to spin-dependent cross-section off neutrons.