Common approaches for direct model predictive control (MPC) for current reference tracking in power electronics suffer from the high computational complexity encountered when solving integer optimal control problems over long prediction horizons. Recently, an alternative method based on approximate dynamic programming showed that it is possible to reduce the computational burden enabling sampling times under 25 μs by shortening the MPC horizon to a very small number of stages while improving the overall controller performance. In this paper we implemented this new approach on a small size FPGA and validated it on a variable speed drive system with a three-level voltage source converter. Time measurements showed that only 5:76 μs are required to run our algorithm for horizon N = 1 and 17:27 μs for N = 2 while outperforming state of the art approaches with much longer horizons in terms of currents distortion and switching frequency. To the authors' knowledge, this is the first time direct MPC for current control has been implemented on an FPGA solving the integer optimization problem in real-time and achieving comparable performance to formulations with long prediction horizons.