The origin of the extragalactic γ-ray background permeating throughout the Universe remains a mystery forty years after its discovery 1 . The extrapolated population of blazars can account for only half of the background radiation in the energy range of ∼0.1-10 GeV (refs 2,3). Here we show that quasar-driven outflows generate relativistic protons that produce the missing component of the extragalactic γ-ray background and naturally match its spectral fingerprint, with a generic break above ∼1 GeV. The associated γ-ray sources are too faint to be detected individually, explaining why they had not been identified so far. However, future radio observations may image their shock fronts directly. Our best fit to the Fermi-LAT observations of the extragalactic γ-ray background spectrum provides constraints on the outflow parameters that agree with observations of these outflows 4-7 and theoretical predictions 8,9 . Although our model explains the data, there might be additional contributing sources.The components of the extragalactic γ-ray background (EGB) have been a puzzle since its discovery four decades ago 10 . Recently, the Large Area Telescope (LAT) on Fermi provided a fifty-month measurement of the integrated emission from γ-ray sources, with photon energies extending from 0.1 to 820 GeV (ref. 2). The latest analysis of Fermi-LAT data implies that both resolved and unresolved blazars account for ∼50 +12 −11 % of the EGB in the energy range of 0.1-10 GeV, leaving the origin of the remaining component in question 3 .Active galactic nuclei (AGN) are observed to exhibit strong outflows, with velocities of ∼0.1c, as manifested by broad absorption lines 5,7 . The ratio between the input kinetic luminosity of the outflows L in and the bolometric luminosity of quasars L bol , f kin , is observationally inferred to be f kin ∼ 1-5% (refs 4-7). The shock wave produced by the interaction of a quasar-driven outflow with the surrounding interstellar medium is expected to accelerate protons to relativistic energies, similarly to the shocks surrounding supernova (SN) remnants, where observations of γ-ray emission due to decay of neutral pion (π 0 ) indicate relativistic proton-proton (pp) collisionsHere, we calculate the analogous γ-ray emission from quasar-driven outflows. The energy distribution of accelerated protons per unit volume can be written as, where E p is the proton energy, N 0 is a normalization constant, and the power-law index Γ p ∼ 2-3, based on theoretical models 12 and observations of shocks around SN remnants 11,13 . We adopt a fiducial value of Γ p ∼ 2.7 and show that our results are not very sensitive to variations around this value (see Supplementary Fig. 1 and we have verified that our results are not sensitive to variations around this value. Here, n p,0 = (n p /1 cm −3 ) is the proton number density, σ pp,−26 = (σ pp /10 −26 cm 2 ) is the inelastic cross section of pp collision, and R s,kpc = (R s /1 kpc) and v s,3 = (v s /10 3 km s −1 ) are the radius and velocity of the outflowing shell, which can ...