[en] Decaying dark matter particles could be indirectly detected as an excess over a simple power law in the energy spectrum of the diffuse extragalactic gamma-ray background. Furthermore, since the Earth is not located at the center of the Galactic dark matter halo, the exotic contribution from dark matter decay to the diffuse gamma-ray flux is expected to be anisotropic, offering a complementary method for the indirect search for decaying dark matter particles. In this paper we discuss in detail the expected dipole-like anisotropies in the dark matter signal, taking also into account the radiation from inverse Compton scattering of electrons and positrons from dark matter decay. A different source for anisotropies in the gamma-ray flux are the dark matter density fluctuations on cosmic scales. We calculate the corresponding angular power spectrum of the gamma-ray flux and comment on observational prospects. Finally, we calculate the expected anisotropies for the decaying dark matter scenarios that can reproduce the electron/positron excesses reported by PAMELA and the Fermi LAT, and we estimate the prospects for detecting the predicted gamma-ray anisotropy in the near future. (orig.)