Recently, many studies indicate that the GeV gamma ray excess signal from the central Milky Way can be best explained by ∼40–50 GeV dark matter annihilating via the b b ¯ channel. However, this model appears to be disfavored by the recent Fermi-LAT data for dwarf spheroidal galaxies and the constraint from synchrotron radiation. In this article, we describe a consistent picture to relieve the tensions between the dark matter annihilation model and the observations. We show that a baryonic feedback process is the key to alleviate the tensions and the ∼40–50 GeV dark matter model is still the best one to account for the GeV gamma ray excess in the Milky Way.