Offshore wind turbines take advantage of the vast energy resource in open waters but face structural integrity challenges specific to their operating environment that require cost-effective load alleviation solutions. This paper introduces a computational methodology for model-based two- and three-dimensional design of load alleviation systems on offshore wind turbines. The aero-hydro-servoelastic model is formulated in a convenient state-space representation, coupling a multi-body composite beam description of the main structural elements with unsteady vortex-lattice aerodynamics and Morison's description of the hydrodynamics. The aerodynamics does not require empirical corrections and focuses on a control-oriented approach to the modelling. Numerical results show that through trailing-edge flaps actuated by a robust controller, more than 60% reduction in dynamic loading due to atmospheric turbulence can be achieved for the sectional model and close to 13% reduction in blade loads is obtained for the complete three-dimensional floating turbine.