This paper develops a novel feedforward control strategy for reducing structural loads caused by waves in floating offshore wind turbines. The proposed control strategy is based on the inversion of a linear model of the floating wind turbine, and a real-time forecast of the wave obtained from an upstream measurement is utilized to compute a collective pitch control action. Two feedforward controllers are considered: one is designed to cancel the rotor speed oscillations and one to lower the towertop fore-aft shear force. The feedforward control strategies are implemented in a 10MW floating wind turbine, complementing the standard feedback controller for generator speed regulation. Numerical simulations are carried out in FAST, in four operating conditions with realistic wind and waves, proving the proposed feedforward controller effectively mitigates the structural loads caused by waves. In detail, the feedforward action reduces the loads spectra in the frequency range where linear wave is active. The best performance is realized higher winds (the FA force is reduced up to 25% in 22 m/s wind), where the wave excitation is the strongest.