In this work we compute for the first time the so-called Complete-NLO predictions for top-quark pair hadroproduction in association with at least one isolated photon (ttγ). We also compute NLO QCD+EW predictions for the similar case with at least two isolated photons (ttγγ) and for single-top hadroproduction in association with at least one isolated photon. In addition, we complement our results with NLO QCD+EW predictions of the hadronic and leptonic decays of top-quark including an isolated photon. All these results have been obtained in a completely automated approach, by extending the capabilities of the MadGraph5_aMC@NLO framework and enabling the Complete-NLO predictions for processes with isolated photons in the final state. We discuss the technical details of the implementation, which involves a mixed EW renormalisation scheme for such processes.