We trace the origin of the newly determined extragalactic gamma-ray background from EGRET data to an unresolved population of blazars and neutralino annihilation in cold dark matter halos. Using results of high-resolution simulations of cosmic structure formation, we calculate composite spectra and compare with the EGRET data. The resulting best-fit value for the neutralino mass is m(chi) = 515(+110)(-75) GeV (systematic errors approximately 30%).