  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.
