The recently detected Fermi Satellite GRBs show two distinct features in their high energy (> 100 MeV) emission. First, the high energy emission is delayed with respect to the detection of the lower energy (sub-MeV) emission. Second, the high energy emission lasts much longer than the lower energy one; the latter shows a sharp decay seen in most of the Swift GRBs. These two features can be explained by the fact that the high energy emission (> 100 MeV) is produced in the external shock via synchrotron emission. This model clearly provides the explanation to the two puzzling discoveries mentioned above: the delay in the high energy emission is explained by the deceleration time of the ejecta, and the long lasting high energy emission reflects the usual power-law decay of the decelerating ejecta emission. Using the data for GRB 080916c, we show that not only the temporal and spectral properties of the long lasting high energy emission are consistent with the external shock origin, but also its magnitude. We also show that the necessary magnetic field is consistent with simply being the compressed magnetic field of the circum-stellar medium. If one extrapolates the early external shock emission to X-ray and optical bands at 1 day, when this data is available from Swift and other ground telescopes, then one finds an excellent agreement. The inverse exercise yields also positive results: using only the X-ray and optical data observed at 1 day and extrapolating it back in time to the high energy band one predicts the detected high energy emission fairly accurately.