By accounting for almost 25% of the capital cost of an OWT (offshore wind turbine), optimisation of support structures provides an efficient way to reduce the currently high cost of offshore wind energy. In this paper, a structural optimisation model for OWT support structures has been developed based on a coupled parametric FEA (Finite Element Analysis) and GA (Genetic Algorithm), minimising the mass of the support structure under multi-criteria constraints. Contrary to existing optimisation models for OWT support structures, the proposed model is an integrated structural optimisation model, which optimises the components of the support structure (i.e. tower, transition piece, grout and monopile) simultaneously. The outer diameters and section thicknesses along the support structure are chosen as design variables. A set of constraints based on multi-criteria design assessment is applied according to standard requirements, which includes vibration, stress, deformation, buckling, fatigue and design variable constraints. The model has been applied to the NREL (National Renewable Energy Laboratory) 5MW OWT on an OC3 (Offshore Code Comparison Collaboration) monopile. The results of the application of the integrated optimisation methodology show a 19.8% reduction in the global mass of the support structure while satisfying all the design constraints. It is demonstrated that the proposed structural optimisation model is capable of effectively and accurately determining the optimal design of OWT support structures, which significantly improves their design efficiency.