  We compute the decoupling relations for the strong coupling, the light quark
masses, the gauge-fixing parameter, and the light fields in QCD with heavy
charm and bottom quarks to three-loop accuracy taking into account the exact
dependence on $m_c/m_b$. The application of a low-energy theorem allows the
extraction of the three-loop effective Higgs-gluon coupling valid for
extensions of the Standard Model with additional heavy quarks from the
decoupling constant of $\alpha_s$.
