  The origin of the diffuse gamma-ray background (DGRB), the one that remains
after subtracting all individual sources from observed gamma-ray sky, is
unknown. The DGRB possibly encompasses contributions from different source
populations such as star-forming galaxies, starburst galaxies, active galactic
nuclei, gamma-ray bursts, or galaxy clusters. Here, we combine cosmological
magnetohydrodynamical simulations of clusters of galaxies with the propagation
of cosmic rays (CRs) using Monte Carlo simulations, in the redshift range
$z\leq 5.0$, and show that the integrated gamma-ray flux from clusters can
contribute up to $100\%$ of the DGRB flux observed by Fermi-LAT above $100$
GeV, for CRs spectral indices $\alpha = 1.5 - 2.5$ and energy cutoffs
$E_{\text{max}} = 10^{16} - 10^{17}$ eV. The flux is dominated by clusters with
masses $10^{13} \lesssim M/M_{\odot} \lesssim 10^{15}$ and redshift $ z
\lesssim 0.3$. Our results also predict the potential observation of
high-energy gamma rays from clusters by experiments like the High Altitude
Water Cherenkov (HAWC), the Large High Altitude Air Shower Observatory
(LHAASO), and potentially the upcoming Cherenkov Telescope Array (CTA).
