An offset-free controller is one that drives controlled outputs to their desired targets at steady state. In the linear model predictive control (MPC) framework, offset-free control is usually achieved by adding step disturbances to the process model. The most widely-used industrial MPC implementations assume a constant output disturbance that can lead to sluggish rejection of disturbances that enter the process elsewhere. This paper presents a general disturbance model that accommodates unmeasured disturbances entering through the process input, state, or output. Conditions that guarantee delectability of the augmented system model are provided, and a steady-state target calculation is constructed to remove the effects of estimated disturbances, Conditions for which offset-free control is possible are stated for the combined estimator, steady-state target calculation, and dynamic controller. Simulation examples are provided to illustrate trade-offs in disturbance model design.