Polymer composites with various recycled poly(ethylene terephthalate)-based (PET-based) polyester matrices (poly(ethylene terephthalate), copolyesters, and unsaturated polyester resins), similar in properties to the primary ones, can be obtained based on PET glycolysis products after purification. PET glycolysis allows one to obtain bis(2-hydroxyethyl) terephthalate and oligo(ethylene terephthalates) with various molecular weights. A kinetic model of poly(ethylene terephthalate) homogeneous glycolysis under the combined or separate action of oligo(ethylene terephthalates), bis(2-hydroxyethyl) terephthalate, and ethylene glycol is proposed. The model takes into account the interaction of bound, terminal, and free ethylene glycol molecules in the PET feedstock and the glycolysis agent. Experimental data were obtained on the molecular weight distribution of poly(ethylene terephthalate) glycolysis products and the content of bis(2-hydroxyethyl) terephthalate monomer in them to verify the model. Homogeneous glycolysis of PET was carried out at atmospheric pressure in dimethyl sulfoxide (DMSO) and N-methyl-2-pyrrolidone (NMP) solvents with catalyst based on antimony trioxide (Sb2O3) under the action of different agents: ethylene glycol at temperatures of 165 and 180 °C; bis(2-hydroxyethyl) terephthalate at 250 °C; and oligoethylene terephthalate with polycondensation degree 3 at 250 °C. Homogeneous step-by-step glycolysis under the successive action of the oligo(ethylene terephthalate) trimer, bis(2-hydroxyethyl) terephthalate, and ethylene glycol at temperatures of 250, 220, and 190 °C, respectively, was also studied. The composition of products was confirmed using FTIR spectroscopy. Molecular weight characteristics were determined using gel permeation chromatography (GPC), the content of bis(2-hydroxyethyl) terephthalate was determined via extraction with water at 60 °C. The developed kinetic model was found to be in agreement with the experimental data and it could be used further to predict the optimal conditions for homogeneous PET glycolysis and to obtain polymer-based composite materials with desired properties.