  We use a recent census of the Milky Way (MW) satellite galaxy population to
constrain the lifetime of particle dark matter (DM). We consider two-body
decaying dark matter (DDM) in which a heavy DM particle decays with lifetime
$\tau$ comparable to the age of the Universe to a lighter DM particle (with
mass splitting $\epsilon$) and to a dark radiation species. These decays impart
a characteristic "kick velocity," $V_{\mathrm{kick}}=\epsilon c$, on the DM
daughter particles, significantly depleting the DM content of low-mass subhalos
and making them more susceptible to tidal disruption. We fit the suppression of
the present-day DDM subhalo mass function (SHMF) as a function of $\tau$ and
$V_{\mathrm{kick}}$ using a suite of high-resolution zoom-in simulations of
MW-mass halos, and we validate this model on new DDM simulations of systems
specifically chosen to resemble the MW. We implement our DDM SHMF predictions
in a forward model that incorporates inhomogeneities in the spatial
distribution and detectability of MW satellites and uncertainties in the
mapping between galaxies and DM halos, the properties of the MW system, and the
disruption of subhalos by the MW disk using an empirical model for the
galaxy--halo connection. By comparing to the observed MW satellite population,
we conservatively exclude DDM models with $\tau < 18\ \mathrm{Gyr}$ ($29\
\mathrm{Gyr}$) for $V_{\mathrm{kick}}=20\ \mathrm{km}\, \mathrm{s}^{-1}$ ($40\
\mathrm{km}\, \mathrm{s}^{-1}$) at $95\%$ confidence. These constraints are
among the most stringent and robust small-scale structure limits on the DM
particle lifetime and strongly disfavor DDM models that have been proposed to
alleviate the Hubble and $S_8$ tensions.
