The gamma -ray sky can be decomposed into individually detected sources, diffuse emission attributed to the interactions of Galactic cosmic rays with gas and radiation fields, and a residual all-sky emission component commonly called the isotropic diffuse gamma -ray background (IGRB). The IGRB comprises all extragalactic emissions too faint or too diffuse to be resolved in a given survey, as well as any residual Galactic foregrounds that are approximately isotropic. The first IGRB measurement with the Large Area Telescope (LAT) on board the Fermi Gamma-ray Space Telescope (Fermi) used 10 months of sky-survey data and considered an energy range between 200 MeV and 100 GeV. Improvements in event selection and characterization of cosmic-ray backgrounds, better understanding of the diffuse Galactic emission (DGE), and a longer data accumulation of 50 months allow for a refinement and extension of the IGRB measurement with the LAT, now covering the energy range from 100 MeV to 820 GeV. The IGRB spectrum shows a significant high-energy cutoff feature and can be well described over nearly four decades in energy by a power law with exponential cutoff having a spectral index of 2.32 + or - 0.02 and a break energy of (279 + or - 52) GeV using our baseline DGE model. The total intensity attributed to the IGRB is (7.2 + or - 0.6) x 10 super(-6) cm super(-2) s super(-1) sr super(-1) above 100 MeV, with an additional +15%/-30% systematic uncertainty due to the Galactic diffuse foregrounds.