- Structure formation in the intergalactic medium (IGM) produces large-scale, collisionless shock waves, in which electrons can be accelerated to highly relativistic energies. Such electrons can Compton-scatter cosmic microwave background photons up to γ-ray energies. We study the radiation emitted in this process using a hydrodynamic cosmological simulation of a ΛCDM universe. The resulting radiation, extending beyond TeV energies, has roughly constant energy flux per decade in photon energy, in agreement with the predictions of Loeb & Waxman. Assuming that a fraction ξe = 0.05 of the shock thermal energy is transferred to the population of accelerated relativistic electrons, as inferred from collisionless nonrelativistic shocks in the interstellar medium, we find that the energy flux of this radiation, 2(dJ/d) 50-160 eV cm-2 s-1 sr-1, constitutes ~10% of the extragalactic γ-ray background flux. The associated γ-ray point sources are too faint to account for the ~60 unidentified EGRET γ-ray sources, but GLAST should detect and resolve several γ-ray sources associated with large-scale IGM structures for ξe 0.03 and many more sources for larger ξe. The intergalactic origin of the shock-induced radiation can be verified through a cross-correlation with, e.g., the galaxy distribution that traces the same structure. Its shock origin may be tested by cross-correlating its properties with radio synchrotron radiation, emitted as the same accelerated electrons gyrate in postshock magnetic fields. We predict that GLAST and Cerenkov telescopes such as MAGIC, VERITAS, and HESS should resolve γ-rays from nearby (redshifts z 0.01) rich galaxy clusters, perhaps in the form of a ~5-10 Mpc diameter ringlike emission tracing the cluster accretion shock, with luminous peaks where the ring intersects galaxy filaments detectable even at z 0.025.