Epoxy modification of asphalt binders has been recognized as a very effective technology to alter the chemistry of asphaltic materials in such a way that long-lasting pavement structures can be designed. However, the phenomena that are involved to build up the physico-mechanical properties of epoxy asphalt systems are still unknown. The focus of this paper is on understanding the link between chemistry and the mechanical properties of epoxy asphalt binders during the thermo-irreversible process of chemical hardening. For this purpose, a constitutive model for predicting the evolution of cure-induced stresses in epoxy asphalt binders is proposed, and an experimental program was developed to determine the model parameters. The cure dependency of physico-mechanical parameters of modified binder was obtained and imported into the model to simulate the build-up of material properties during (non-)isothermal hardening of epoxy asphalt binder. The model is implemented in a commercially finite element tool by coupling the chemical, thermal, and mechanical phenomena with multi-physics strategies, and the results are analyzed to identify the influence of different heating conditions on the crosslinking density and subsequently on stress build-up. It was found that the amount of stress build-up during curing was strongly dependent on the heating conditions, and a higher rate of stress build-up was observed at higher applied temperatures. In other words, the processing conditions during in-plant material production or in-field manufacturing of structures made by epoxy asphalt systems affect the material hardening and subsequently the desired functionalities of pavement structures.