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We propose a model predictive control (MPC) strategy with guaranteed performance bounds for three-phase inverters with linear loads. The MPC technique is combined with space vector modulation (SVM) to reduce the harmonic content of the generated signals. The key contributions of this article are the development of computationally efficient algorithms to implement the proposed technique; the extension to the use of arbitrary control and prediction horizons; an analysis of the closed loop stability of the system; and the obtention of a ultimate bound on the error between the reference signal and the controlled output. The proposed controller is tested in simulation on a three-phase inverter with an LCL filter.