Significance We develop a physics-based earthquake-forecasting model for evaluating seismic hazard due to fluid injection, considering both pore pressure and poroelastic stresses. Applying this model to complex settings like Oklahoma, we show that the regional induced earthquake timing and magnitude are controlled by the process of fluid diffusion in a poroelastic medium, and thus seismicity can be successfully forecasted by using a rate-and-state earthquake nucleation model. We find that pore-pressure diffusion controls the induced earthquakes in Oklahoma. However, its impact is enhanced by poroelastic effects. This finding has significant implications for induced earthquake-forecasting efforts by integrating the physics of fluid diffusion and earthquake nucleation.