  We present the calculation of the next-to-leading contribution of order
$\alpha_S^2\alpha^2$ to the production of a Standard Model Higgs boson in
association with a top-quark pair at hadron colliders. All effects of weak and
QCD origin are included, whereas those of QED origin are ignored. We work in
the MadGraph5_aMC@NLO framework, and discuss sample phenomenological
applications at a 8, 13, and 100 TeV $pp$ collider, including the effects of
the dominant next-to-leading QCD corrections of order $\alpha_S^3\alpha$.
