The two-loop quantum chromodynamics (QCD) radiative corrections to the Bc meson leptonic decay rate are calculated in the framework of the non-relativistic QCD (NRQCD) factorization formalism. Two types of master integrals appearing in the calculation are obtained analytically for the first time. We calculate the short-distance coefficient of the leading matrix element to order αs2 by matching the full perturbative QCD calculation results to the corresponding NRQCD results. The result presented in this work helps the evaluation of both the Bc leptonic decay constant and the Cabibbo–Kobayashi–Maskawa (CKM) matrix element |Vcb| to the full next-to-next-to-leading-order (NNLO) degree of accuracy.