This article focuses on the control of an actuated knee joint orthosis. The proposed solution is a novel model predictive control framework dedicated to assistive and rehabilitation purposes. This framework includes 1) an exact input-to-state feedback linearization, 2) a model predictive controller (MPC or EMPC), considering input/output constraints, 3) a least-squares dynamic parameters identification, 4) a nonlinear disturbance observer for the estimation of the wearer's torque, 5) a Lyapunov-based stability analysis of the resulting closed-loop system, and 6) a reference trajectory generator. The proposed framework has been validated via real-time experiments performed on three healthy subjects wearing the knee joint orthosis. Various experimental scenarios have been considered, including assistive and resistive rehabilitation tasks in a sitting position and walking with normal/abnormal gait patterns. The obtained results indicate the efficiency of the proposed predictive controllers with respect to a conventional proportional-integral-derivative (PID) controller in terms of tracking performance, required torque, and wearer comfort.