Numerical models of the tidal disruption of the Sagittarius (Sgr) dwarf galaxy have recently been developed that for the first time simultaneously satisfy most observational constraints on the angular position, distance, and radial velocity trends of both leading and trailing tidal streams emanating from the dwarf. We use these dynamical models in combination with extant 3-D position and velocity data for Galactic globular clusters and dSph galaxies to identify those Milky Way satellites that are likely to have originally formed in Sgr and been stripped from it during its extended interaction with the Milky Way. We conclude that the globular clusters Arp 2, M 54, NGC 5634, Terzan 8, and Whiting 1 are likely associated with the Sgr dwarf, and that Berkeley 29, NGC 5053, Pal 12, and Terzan 7 may be as well. The initial Sgr system therefore may have contained 5-9 globular clusters, corresponding to a specific frequency S_N = 5 - 9 for an initial Sgr luminosity M_V = -15.0. Our result is consistent with the 8\pm2 Sgr globular clusters expected from statistical modeling of the Galactic globular cluster distribution and the corresponding false-association rate due to chance alignments with the Sgr streams. These clusters are consistent with previous reconstructions of the Sgr age-metallicity relation, and show no evidence for a second-parameter effect shaping their horizontal branch morphologies. We find no statistically significant evidence to suggest that any of the recently discovered population of ultra-faint dwarf galaxies are conclusively associated with the Sgr tidal streams. (Abridged).
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