  In this work we derive the first theoretical prediction of the
cross-correlation signal between the unresolved gamma-ray background and the
21-cm line originated by the spin-flip transition of neutral hydrogen atoms, by
taking as benchmark experiment the space telescope {\it Fermi}-LAT for gamma
rays and the next-generation radio telescope Square Kilometer Array (SKA) as
well as its precursor MeerKAT for the 21-cm emission. The attainable bounds in
the dark matter (DM) parameter space are envisioned to be competitive already
with the combination {\it Fermi}-LAT $\times$ MeerKAT, but SKA will allow to go
deeper and probe a thermal DM particle up to masses of 130 GeV. A future
gamma-ray detector with better angular resolution and larger exposure together
with an ungraded radio telescope will have the potentiality to probe a DM
candidate with thermal annihilation cross-section and masses up to the TeV
scale.
