In this work, an environmentally-friendly leaching process for the recovery of indium (In) and tin (Sn) from LCD panel waste was investigated. Easily degradable citrates (C6H5O7 3−), i.e., sodium citrate and citric acid, were used as complexing agents. The morphology and composition of the species present in the LCD powder before and after the leaching processes were characterized by scanning electron microscopy (SEM) and energy dispersive spectroscopy (EDS). The concentrations of In, Sn, and iron (Fe) present in the leachate were determined by atomic absorption spectrometry (AAS). The necessary thermodynamic conditions for achieving substantial In recovery were established by using MEDUSA software. The optimal process conditions were determined experimentally by varying the initial citrate concentration as well as by using reducing or oxidizing media, respectively hydrazine (N2H4) or hydrogen peroxide (H2O2). It was found that using N2H4 in a citrate solution as a reducing agent enhances the leaching efficiency. However, high concentrations of Sn and Fe with respect to In were found in the LCD powder. Therefore, a pretreatment processes to first remove the excess of Sn and Fe, which compete with In for the citrate, was implemented. Leaching with 1 M citrate, 0.2 M N2H4, at pH = 5, using sodium hydroxide (NaOH) at solid:liquid (S:L) ratio of 20 g∙L−1, yielded a remarkably high In recovery of 98.9% after 16.6 h.