The present work deals with the numerical simulation of the precipitation kinetics of δ (Ni3(Nb, Al)) and γ′ (Ni 3(Al, Ti, Nb)) phases in the commercial nickel-base superalloy ATI Allvac®718Plus™. Important precipitate parameters such as volume fraction, mean radius and number density are numerically calculated as a function of the heat treatment parameters time and temperature and compared to experimentally determined data. To match the experimentally observed kinetics, the predicted interfacial energy of the precipitates, as calculated for a sharp, planar phase boundary, is adjusted to take into account the interfacial curvature and entropic effects of a diffuse interface. Using these modified interfacial energies, the calculated results show excellent agreement with the experimental measurements. Finally, a calculated time-temperature-precipitation (TTP) diagram for concurrent δ and γ′ precipitation is presented, which clearly demonstrates strong kinetic interactions during simultaneous precipitation of these phases. Thus, the present study emphasizes the importance of carefully controlling the heat treatment parameters time and temperature during the production process of ATI Allvac®718Plus™, in order to achieve the desired microstructure and hence mechanical properties.