The interaction properties of cold dark matter (CDM) particle candidates, such as those of weakly interacting massive particles (WIMPs), generically lead to the structuring of dark matter on scales much smaller than typical galaxies, potentially down to $sim 10^{-10}M_odot$. This clustering translates into a very large population of subhalos in galaxies and affects the predictions for direct and indirect dark matter searches (gamma rays and antimatter cosmic rays). In this paper, we elaborate on previous analytic works to model the Galactic subhalo population, while consistently with current observational dynamical constraints on the Milky Way. In particular, we propose a self-consistent method to account for tidal effects induced by both dark matter and baryons. Our model does not strongly rely on cosmological simulations as they can hardly be fully matched to the real Milky Way, but for setting the initial subhalo mass fraction. Still, it allows to recover the main qualitative features of simulated systems. It can further be easily adapted to any change in the dynamical constraints, and be used to make predictions or derive constraints on dark matter candidates from indirect or direct searches. We compute the annihilation boost factor, including the subhalo-halo cross-product. We confirm that tidal effects induced by the baryonic components of the Galaxy play a very important role, resulting in a local average subhalo mass density $lesssim 1%$ of the total local dark matter mass density, while selecting in the most concentrated objects and leading to interesting features in the overall annihilation profile in the case of a sharp subhalo mass function. Values of global annihilation boost factors range from $sim 2$ to $sim 20$, while the local annihilation rate is about half as much boosted.
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