  The central region of the Milky Way is one of the foremost locations to look
for dark matter (DM) signatures. We report the first results on a search for DM
particle annihilation signals using new observations from an unprecedented
gamma-ray survey of the Galactic Center (GC) region, ${\it i.e.}$, the Inner
Galaxy Survey, at very high energies ($\gtrsim$ 100 GeV) performed with the
H.E.S.S. array of five ground-based Cherenkov telescopes. No significant
gamma-ray excess is found in the search region of the 2014-2020 dataset and a
profile likelihood ratio analysis is carried out to set exclusion limits on the
annihilation cross section $\langle \sigma v\rangle$. Assuming Einasto and
Navarro-Frenk-White (NFW) DM density profiles at the GC, these constraints are
the strongest obtained so far in the TeV DM mass range. For the Einasto
profile, the constraints reach $\langle \sigma v\rangle$ values of $\rm
3.7\times10^{-26} cm^3s^{-1}$ for 1.5 TeV DM mass in the $W^+W^-$ annihilation
channel, and $\rm 1.2 \times 10^{-26} cm^3s^{-1}$ for 0.7 TeV DM mass in the
$\tau^+\tau^-$ annihilation channel. With the H.E.S.S. Inner Galaxy Survey,
ground-based $\gamma$-ray observations thus probe $\langle \sigma v\rangle$
values expected from thermal-relic annihilating TeV DM particles.
