Floating wind turbines rely on feedback-only control strategies to mitigate the negative effects of wave excitation. Improved power generation and lower fatigue loads can be achieved by including information about incoming waves in the turbine controller. In this paper, a wave-feedforward control strategy is developed and implemented in a 10 MW floating wind turbine. A linear model of the floating wind turbine is established and utilized to understand how wave excitation affects rotor speed and so power, as well as to show that collective pitch is suitable for reducing the effects of wave excitation. A feedforward controller is designed based on the inversion of the linear model, and a gain-scheduling algorithm is proposed to adapt the feedforward action as wind speed changes. The performance of the novel wave-feedforward controller is examined first by means of linear analysis and then with non-linear time-domain simulations in FAST. This paper proves that including some information about incoming waves in the turbine controller can play a crucial role in improving power quality and the turbine fatigue life. In particular, the proposed wave-feedforward control strategy achieves this goal complementing the industry-standard feedback pitch controller. Together with the wave-feedforward control strategy, this paper provides some insights about the response of floating wind turbines to collective-pitch control and waves, which could be useful in future control-design studies.