Abstract: We present a new global fit of the 19-dimensional phenomenological Minimal Supersymmetric Standard Model (pMSSM-19) that complies 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 similar to 80 – 100 GeV annihilating into WW with a branching ratio of 95%; the second to heavier neutralinos, with mass similar to 180 – 200 GeV annihilating into (l) over barl 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.