This paper proposes a multi-objective optimal control and switching strategy for floating offshore wind turbines when the wind speed can be approximately predicted. The system is modeled as a hybrid automaton with two modes corresponding to the turbine operation in low- and high-speed wind profiles. The main control objective in the low-speed wind mode is to maximize the total captured power in a finite time horizon, whereas in the high-speed mode, it is desired to regulate the generator torque and speed around predefined rated values even under gust loads. The problem is formulated as a constrained mixed-integer bilinear program in a model predictive control framework. The posed constraints correspond to the electrical/mechanical limitations of the blade actuators and generators. Various practical considerations, such as minimizing the number of switching occurrences and mechanical fatigue prevention, are explicitly considered in the optimization problem. The proposed control method is applied to the dynamical model of a real wind turbine and simulation results are presented.