The latest forecasts on the upcoming effects of climate change are leading to a change in the worldwide power production model, with governments promoting clean and renewable energies, as is the case of tidal energy. Nevertheless, it is still necessary to improve the efficiency and lower the costs of the involved processes in order to achieve a Levelized Cost of Energy (LCoE) that allows these devices to be commercially competitive. In this context, this paper presents a novel complementary control strategy aimed to maximize the output power of a Tidal Stream Turbine (TST) composed of a hydrodynamic turbine, a Doubly-Fed Induction Generator (DFIG) and a back-to-back power converter. In particular, a global control scheme that supervises the switching between the two operation modes is developed and implemented. When the tidal speed is low enough, the plant operates in variable speed mode, where the system is regulated so that the turbo-generator module works in maximum power extraction mode for each given tidal velocity. For this purpose, the proposed back-to-back converter makes use of the field-oriented control in both the rotor side and grid side converters, so that a maximum power point tracking-based rotational speed control is applied in the Rotor Side Converter (RSC) to obtain the maximum power output. Analogously, when the system operates in power limitation mode, a pitch angle control is used to limit the power captured in the case of high tidal speeds. Both control schemes are then coordinated within a novel complementary control strategy. The results show an excellent performance of the system, affording maximum power extraction regardless of the tidal stream input.