The General Antiparticle Spectrometer (GAPS) experiment is designed to detect low-energy (< 0.25 GeV/n) cosmic-ray antinuclei as indirect signatures of dark matter. Several beyond-the-standard-model scenarios predict a large antideuteron flux due to dark matter decay or annihilation compared to the astrophysical background. The GAPS experiment will perform such measurements using long-duration balloon flights over Antarctica, beginning in the 2022/23 austral summer. The experimental apparatus consists of ten planes of Si(Li) detectors surrounded by a time-of-flight system made of plastic scintillators. The detection of the primary antinucleus relies on the reconstruction of the annihilation products: the low-energy antinucleus is captured by an atom of the detector material, forming an exotic atom that de-excites by emitting characteristics X-rays. Finally, the antinucleus undergoes nuclear annihilation, producing a “star” of pions and protons emitted from the annihilation vertex. Several algorithms were developed to determine the annihilation vertex position and to reconstruct the topology of the primary and secondary particles. An overview of the event reconstruction techniques and their performances, based on detailed Monte Carlo simulation studies, will be presented in this contribution.