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We report on the observations of four well-localized binary black hole (BBH)mergers by the High Energy Stereoscopic System (H.E.S.S.) during the second andthird observing runs of Advanced LIGO and Advanced Virgo, O2 and O3. H.E.S.S.can observe $\mathrm{20\,deg^2}$ of the sky at a time and follows upgravitational-wave (GW) events by ``tiling'' localization regions to maximizethe covered localization probability. During O2 and O3, H.E.S.S. observed largeportions of the localization regions, between 35\% and 75\%, for four BBHmergers (GW170814, GW190512\_180714, GW190728\_064510, and S200224ca). Forthese four GW events, we find no significant signal from a pointlike source inany of the observations, and set upper limits on the very high energy ($>$100GeV) $\gamma$-ray emission. The 1-10 TeV isotropic luminosity of these GWevents is below $10^{45}$ erg s$^{-1}$ at the times of the H.E.S.S.observations, around the level of the low-luminosity GRB 190829A. Assuming nochanges are made to how follow-up observations are conducted, H.E.S.S. canexpect to observe over 60 GW events per year in the fourth GW observing run,O4, of which eight would be observable with minimal latency.

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H.E.S.S. follow-up observations of Binary Black Hole Coalescence events  during the second and third Gravitational Waves observing runs of Advanced  LIGO and Advanced Virgo