For the newly discovered W-boson mass anomaly, one of the simplest dark matter (DM) models that can account for the anomaly without violating other astrophysical and experimental constraints is the inert two Higgs doublet model, in which the DM mass (m_{S}) is found to be within ∼54-74 GeV. In this model, the annihilation of DM via SS→bb[over ¯] and SS→WW^{*} would produce antiprotons and gamma rays, and may account for the excesses identified previously in both particles. Motivated by this, we reanalyze the AMS-02 antiproton and Fermi-LAT Galactic center γ-ray data. For the antiproton analysis, the novel treatment is the inclusion of the charge-sign-dependent three-dimensional solar modulation model as constrained by the time-dependent proton data. We find that the excess of antiprotons is more distinct than previous results based on the force-field solar modulation model. The interpretation of this excess as the annihilation of SS→WW^{*} (SS→bb[over ¯]) requires a DM mass of ∼40-80 (40-60) GeV and a velocity-averaged cross section of O(10^{-26}) cm^{3} s^{-1}. As for the γ-ray data analysis, besides adopting the widely used spatial template fitting, we employ an orthogonal approach with a data-driven spectral template analysis. The fitting to the GeV γ-ray excess yields DM model parameters overlapped with those to fit the antiproton excess via the WW^{*} channel. The consistency of the DM particle properties required to account for the W-boson mass anomaly, the GeV antiproton excess, and the GeV γ-ray excess suggests a common origin of them.