Passive tuned mass dampers (TMDs) have been increasingly investigated for vibration control of wind turbines. However, TMD designs based on individual or a few operating conditions may result in insufficient consideration of the TMDs impact on wind turbines. For instance, the influence of end-stop collision forces on the main structural damage may be significantly underestimated, thereby affecting the overall lifecycle evaluation. In this study, focusing on large offshore fixed-bottom monopile wind turbines, we propose an integrated TMD design methodology taking the damper displacement constraints into full account. A comprehensive optimization of the passive omnidirectional pendulum-type TMD is conducted considering large number of operating conditions in the offshore environment. Next, a real-world application of the optimally designed TMD is performed for a 6450 kW monopile offshore wind on the Yellow Sea, China. We develop an on-site testing methodology and evaluation criteria for assessing the effectiveness of the TMD offshore. The results of resonance, emergency stop, operatingand reliability test conditions demonstrate the following: under the optimized TMD design taking into account all operating conditions, the TMD with a mass ratio of 1.56% can offer added damping in the fore-aft and side-side directions of the turbine, and provides the desired damping ratio of 1%; within a 4% frequency range around the design frequency, the TMD achieves effective vibration control; at rated power, the TMD achieves a reduction of more than 50% in the amplitude of the tower base side-side bending moment (Mx). The integrated TMD design with displacement constraints allows for the optimal TMD design across all operating conditions, thereby achieving superior overall vibration control and reduction in fatigue loads. The successful real-world application of the TMD based on integrated design methodology is of high value to the research community.