This paper presents a non-linear model predictive control approach for offset-free tracking and the rejection of piece-wise constant disturbances. The approach involves augmenting the system’s state vector with the integral of the tracking error, enabling the design of a non-linear model predictive controller for this augmented system. Nominal closed-loop stability is enforced thanks to a terminal equality constraint and proven by a Lyapunov argument. Compared to the existing offset-free approaches in the literature, our method offers greater simplicity, as it does not rely on linear approximations of the system to control. Furthermore, it eliminates the need to estimate disturbances, a task that is especially challenging with non-linear systems. Comprehensive simulations and experimental tests are conducted according to a non-linear, coupled, two-tank laboratory experiment, demonstrating the robustness and effectiveness of the proposed approach.