The origin of the extragalactic $gamma$-ray background (EGB) has been debated for some time. { The EGB comprises the $gamma$-ray emission from resolved and unresolved extragalactic sources, such as blazars, star-forming galaxies and radio galaxies, as well as radiation from truly diffuse processes.} This letter focuses on the blazar source class, the most numerous detected population, and presents an updated luminosity function and spectral energy distribution model consistent with the blazar observations performed by the {it Fermi} Large Area Telescope (LAT). We show that blazars account for 50$^{+12}_{-11}$,% of the EGB photons ($>$0.1,GeV), and that {it Fermi}-LAT has already resolved $sim$70,% of this contribution. Blazars, and in particular low-luminosity hard-spectrum nearby sources like BL Lacs, are responsible for most of the EGB emission above 100,GeV. We find that the extragalactic background light, which attenuates blazars high-energy emission, is responsible for the high-energy cut-off observed in the EGB spectrum. Finally, we show that blazars, star-forming galaxies and radio galaxies can naturally account for the amplitude and spectral shape of the background in the 0.1--820,GeV range, leaving only modest room for other contributions. This allows us to set competitive constraints on the dark-matter annihilation cross section.
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