In recent years, magnetoelectric (ME) composites have become a demanding research area due to their advancement in practical applications such as miniatured electronic devices, pressure sensors, energy harvesters, spintronics, and gyrators. Since the naturally available single phase ME materials exhibit low ME coupling coefficient and low operational temperature, limiting them in practical applications, artificial ME composites have been developed to observe strong ME coupling and transition temperatures above room temperature. The voltage output in these composites is generally governed by the stress and magnetization state of the magneto-strictive phase, which needs to be characterized effectively. A three-dimensional magneto-strictive constitutive model is used to predict the magneto-strictive behavior, later implemented in COMSOL Multiphysics® using the external material module. The analytical solutions are used to validate the finite element(FE) solutions. Further, the model obtains FE solutions for the ME response of press-fit composites subjected to general magneto-thermo-mechanical loading. Experiments are carried out on the press-fit composite to validate the voltage response predicted by the developed model, which shows good concordance. The developed FE model is used to conduct a parametric study to quantify the effect of external loading conditions, the shape of inclusion, and the field orientation to optimize the ME response in press-fit ME composites. Further, the proposed models are extended to predict the combined effect of stress and temperature on the frequency response of press-fit ME composites.