Analysis of field failure data collected from various wind farm databases indicates that the power converters are among the most critical components in offshore wind turbines, since they suffer from a high failure rate. One efficient approach to enhance the reliability and availability of the wind power systems is through using a redundant converter design, in which a set of power converters is placed together in parallel. The main advantage of a multiple parallel converter system is that the failure of one converter will not necessarily lead to the failure of the entire system. It may however increase the wind turbine's acquisition cost, volume, and weight. In this paper, we propose an approach of joint redundancy and maintenance strategy optimization for offshore wind power converters, aiming to simultaneously determine the "optimal allocation of redundant converters" and the "optimal threshold number of converters that are allowed to fail before sending a maintenance crew to the offshore platform". The optimal solution under various systemlevel constraints (such as reliability, weight, and the available space in nacelle) is derived and the conditions required to make using a redundant system beneficial are discussed. The proposed design is applied to an offshore wind turbine system and its performance is evaluated using a Monte-Carlo simulation technique. Finally, the results are compared with the conventional power converter system and a sensitivity analysis is conducted in order to make the proposed approach applicable for the next generation of wind turbines.