We report on the first Fermi Large Area Telescope (LAT) measurements of the so-called "extra-galactic" diffuse gamma-ray emission (EGB). This component of the diffuse gamma-ray emission is generally considered to have an isotropic or nearly isotropic distribution on the sky with diverse contributions discussed in the literature. The derivation of the EGB is based on detailed modelling of the bright foreground diffuse Galactic gamma-ray emission (DGE), the detected LAT sources and the solar gamma-ray emission. We find the spectrum of the EGB is consistent with a power law with differential spectral index g = 2.41+/-0.05 and intensity, I(> 100 MeV) = (1.03+/-0.17) 10^-5 cm^-2 s^-1 sr^-1, where the error is systematics dominated. Our EGB spectrum is featureless, less intense, and softer than that derived from EGRET data. Show Partial Abstract