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PSR B1259-63/LS 2883 is a gamma-ray binary system consisting of a pulsar inan eccentric orbit around a bright Oe stellar-type companion star that featuresa dense circumstellar disc. The high- and very-high-energy (HE, VHE) gamma-rayemission from PSR B1259-63/LS 2883 around the times of its periastron passageare characterised, in particular, at the time of the HE gamma-ray flaresreported to have occurred in 2011, 2014, and 2017. Spectra and light curveswere derived from observations conducted with the H.E.S.S.-II array in 2014 and2017.  A local double-peak profile with asymmetric peaks in the VHE light curve ismeasured, with a flux minimum at the time of periastron $t_p$ and two peakscoinciding with the times at which the neutron star crosses the companion'scircumstellar disc ($\sim t_p \pm 16$ d). A high VHE gamma-ray flux is alsoobserved at the times of the HE gamma-ray flares ($\sim t_p + 30$ d) and atphases before the first disc crossing ($\sim t_p - 35$ d). PSR B1259-63/LS 2883displays periodic flux variability at VHE gamma-rays without clear signaturesof super-orbital modulation in the time span covered by H.E.S.S. observations.In contrast, the photon index of the measured power-law spectra remainsunchanged within uncertainties for about 200 d around periastron. Lower limitson exponential cut-off energies up to $\sim 40$ TeV are placed.  At HE gamma-rays, PSR B1259-63/LS 2883 has now been detected also before andafter periastron, close to the disc crossing times. Repetitive flares withdistinct variability patterns are detected in this energy range. Such outburstsare not observed at VHEs, although a relatively high emission level ismeasured. The spectra obtained in both energy regimes displays a similar slope,although a common physical origin either in terms of a related particlepopulation, emission mechanism, or emitter location is ruled out.

H.E.S.S. and Fermi-LAT observations of PSR B1259-63/LS 2883 during its 2014 and 2017 periastron passages