Most Fermi gamma-ray burst spectra appear as either a broken power law extending to GeV energies or as a broken power with a separate GeV power-law component. Here we show that such spectra can be understood in terms of magnetically dominated relativistic jets where a dissipative photosphere produces the prompt MeV emission, which is extended into the GeV range by inverse Compton scattering in the external shock, with possible contributions from a reverse shock as well. The bulk Lorentz factors required in these models are in the range of 300-600, and the MeV-GeV time delays arise naturally. In some cases an optical flash and a sub-dominant thermal component are also present.
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