We present quantitative predictions for the detectability of individual Galactic dark matter subhalos in gamma rays from dark matter pair annihilations in their centers. Our method is based on a hybrid approach, employing the highest resolution numerical simulations available (including the recently completed 1 billion particle Via Lactea II simulation), as well as analytical models, for extrapolating beyond the simulations' resolution limit. We include a self-consistent treatment of subhalo boost factors, motivated by our numerical results, and a realistic treatment of the expected backgrounds that individual subhalos must outshine. We show that for reasonable values of the dark matter particle physics parameters (image - 500 GeV and image -10 super(-25) cm super(3) s super(-1)) GLAST may very well discover a few, even up to several dozen, such subhalos at 5 capital sigma significance, and some at more than 20 capital sigma . We predict that the majority of luminous sources would be resolved with GLAST's expected angular resolution. For most observer locations, the angular distribution of detectable subhalos is consistent with a uniform distribution across the sky. The brightest subhalos tend to be massive (median V sub(max) of 24 km s super(-1)) and therefore likely hosts of dwarf galaxies, but many subhalos with V sub(max) as low as 5 km s super(-1) are also visible. Typically detectable subhalos are 20-40 kpc from the observer, and only a small fraction are closer than 10 kpc. The total number of observable subhalos has not yet converged in our simulations, and we estimate that we may be missing up to 3/4 of all detectable subhalos.