The inverse Compton (IC) scattering of ultrarelativistic electrons accelerated at the pulsar wind termination shock is generally believed to be responsible for TeV gamma-ray signal recently reported from the binary system PSR B1259−63/SS2883. While this process can explain the energy spectrum of the observed TeV emission, the gamma-ray fluxes detected by the Array of Imaging Atmospheric Cherenkov Telescopes (HESS) at different epochs do not agree with the published theoretical predictions of the TeV light curve. The main objective of this paper is to show that the HESS results can be explained, under certain reasonable assumptions concerning the cooling of relativistic electrons, by IC scenarios of gamma-ray production in PSR B1259−63. In this paper we study evolution of the energy spectra of relativistic electrons under different assumptions about the acceleration and energy-loss rates of electrons, and the impact of these processes on the light curve of IC gamma-rays. We demonstrate that the observed TeV light curve can be explained (i) by adiabatic losses which dominate over the entire trajectory of the pulsar with a significant increase towards the periastron or (ii) by the ‘early’ (sub-TeV) cut-offs in the energy spectra of electrons due to the enhanced rate of Compton losses close to the periastron. The first four data points obtained just after periastron comprise an exception – possibly due to interaction with the Be star disc, which introduces additional physics not included in the presented model. The calculated spectral and temporal characteristics of the TeV radiation provide conclusive tests to distinguish between these two working hypotheses. The Compton deceleration of the electron–positron pulsar wind contributes to the decrease of the non-thermal power released in the accelerated electrons after the wind termination, and thus to the reduction of the IC and synchrotron components of radiation close to the periastron. Although this effect alone cannot explain the observed TeV and X-ray light curves, the Comptonization of the cold ultrarelativistic wind leads to the formation of gamma-radiation with a specific line-type energy spectrum. While the HESS data already constrain the Lorentz factor of the wind, Γ≤ 106 (for the most likely orbit inclination angle i= 35°, and assuming an isotropic pulsar wind), future observations of this object with GLAST should allow a deep probe of the wind Lorentz factor in the range between 104 and 106.