© 2018 IOP Publishing Ltd and Sissa Medialab. The (x, y) position reconstruction method used in the analysis of the complete exposure of the Large Underground Xenon (LUX) experiment is presented. The algorithm is based on a statistical test that makes use of an iterative method to recover the photomultiplier tube (PMT) light response directly from the calibration data. The light response functions make use of a two dimensional functional form to account for the photons reflected on the inner walls of the detector. To increase the resolution for small pulses, a photon counting technique was employed to describe the response of the PMTs. The reconstruction was assessed with calibration data including 83mKr (releasing a total energy of 41.5 keV) and 3H (andbeta;- with Q = 18.6 keV) decays, and a deuterium-deuterium (D-D) neutron beam (2.45 MeV) . Within the detector's fiducial volume, the reconstruction has achieved an (x, y) position uncertainty of andsigma; = 0.82 cm and andsigma; = 0.17 cm for events of only 200 and 4,000 detected electroluminescence photons respectively. Such signals are associated with electron recoils of energies andsim;0.25 keV and andsim;10 keV, respectively. The reconstructed position of the smallest events with a single electron emitted from the liquid surface (22 detected photons) has a horizontal (x, y) uncertainty of 2.13 cm.