Offshore wind turbine (OWT) structures are highly sensitive to complex ambient excitations, especially extreme winds. To mitigate the vibrations of OWT structures under windstorm or typhoon conditions, a new eddy current with tuned mass damper (EC-TMD) system that combines the advantages of the eddy current damper and the tuned mass damper is proposed to install at the top of them. In the present study, the electromagnetic theory is applied to estimate the damping feature of the eddy current within the EC-TMD system. Then, the effectiveness of the EC-TMD system for vibration mitigation is demonstrated by small-scale tests. Furthermore, the EC-TMD system is used to alleviate structural vibrations of the OWT supported by composite bucket foundations (CBF) under extreme winds at the Xiangshui Wind Farm of China. It is found that the damping of the EC-TMD system can be ideally treated as having linear viscous damping characteristics, which are influenced by the gaps between the permanent magnets and the conductive materials as well as the permanent magnet layouts. Meanwhile, the RMS values of displacements of the OWT structure can be mitigated by 16% to 28%, and the acceleration can also be reduced significantly. Therefore, the excellent vibration-reducing performance of the EC-TMD system is confirmed, which provides meaningful guidance for application in the practical engineering of OWTs.