  We report the measurement of the two-neutrino double-beta ($2\nu\beta\beta$)
decay of $^{100}$Mo to the ground state of $^{100}$Ru using lithium molybdate
(\crystal) scintillating bolometers. The detectors were developed for the
CUPID-Mo program and operated at the EDELWEISS-III low background facility in
the Modane underground laboratory. From a total exposure of $42.235$
kg$\times$d, the half-life of $^{100}$Mo is determined to be
$T_{1/2}^{2\nu}=[7.12^{+0.18}_{-0.14}\,\mathrm{(stat.)}\pm0.10\,\mathrm{(syst.)}]\times10^{18}$
years. This is the most accurate determination of the $2\nu\beta\beta$
half-life of $^{100}$Mo to date. We also confirm, with the statistical
significance of $>3\sigma$, that the single-state dominance model of the
$2\nu\beta\beta$ decay of $^{100}$Mo is favored over the high-state dominance
model.
