A model of alloying in the three-layer thin-film system at the low temperature is constructed. Solid solution formation takes place as a result of the diffusion-induced grain boundary migration (DIGM). The unknown parameters are determined from the set of the equations for: (1) grain boundary diffusion along the moving planar phase boundary; (2) the entropy balance in the region of the phase transformation moving with constant velocity; (3) the maximum rate of the free energy release. We consider the model system with complete solubility of the components. The main parameters are self-consistently determined using thermodynamic and kinetic description in the frame of the regular solution model. The model allows determining the concentration distribution along the planar moving phase boundary, its velocity, the thickness of the forming solid solution layer and the limiting average concentration in this layer.