The kinetics of the solid-state reaction between nanolayers of polycrystalline copper and amorphous silicon (a-Si) has been studied in a Cu/a-Si thin-film system by the methods of electron diffraction and simultaneous thermal analysis (STA), including the methods of differential scanning calorimetry (DSC) and thermogravimetry (TG). It has been established that, in the solid-state reaction, two phases are formed in a sequence: Cu + Si → η″-Cu3Si → γ-Cu5Si. It has been shown that the estimated values of the kinetic parameters of the formation processes for the phases η″-Cu3Si and γ-Cu5Si, obtained using electron diffraction, are in good agreement with those obtained by DSC. The formation enthalpy of the phases η″-Cu3Si and γ-Cu5Si has been estimated to be: ΔHη″-Cu3Si = −12.4 ± 0.2 kJ/mol; ΔHγ-Cu5Si = −8.4 ± 0.4 kJ/mol. As a result of the model description of the thermo-analytical data, it has been found that the process of solid-state transformations in the Cu/a-Si thin-film system under study is best described by a four-stage kinetic model R3 → R3 → (Cn-X) → (Cn-X). The kinetic parameters of formation of the η″-Cu3Si phase are the following: Ea = 199.9 kJ/mol, log(A, s−1) = 20.5, n = 1.7; and for the γ-Cu5Si phase: Ea = 149.7 kJ/mol, log(A, s−1) = 10.4, n = 1.3, with the kinetic parameters of formation of the γ-Cu5Si phase being determined for the first time.