Floating Offshore Wind Turbines (FOWTs) have emerged as a promising technology for generating clean energy in deep water locations. Bluewater Energy Services proposes a Tension Leg Platform (TLP) as the floating support structure. An effective Structural Health Monitoring (SHM) system (of which there are various types) can facilitate timely interventions and optimize inspection and maintenance activities by providing continuous insights into their structural condition. Fatigue damage is especially critical for the support structures of FOWTs, as they are subject to cyclic loads that can cause structural damage. This research proposes a fatigue monitoring system for a TLP supporting FOWTs. The methodology used is Modal Decomposition and Expansion (MDE). Due to the complexity of the studied structure in terms of structural dynamics, MDE is selected for its ability to capture dynamic behaviour. The main objective of the fatigue monitoring system is to perform the full-field strain estimation based on a limited number of sensors. This could also allow for the verification of the design considerations. With the presented response reconstruction approach, the stress in the locations prone to fatigue of the platform can be monitored and therefore, enabling estimation of the remaining lifetime of the structure and optimize maintenance planning. Different analytical and numerical models are used in this investigation. The application of MDE in a simple structure (i.e. a cantilever beam) is first assessed to verify the performance and to gain insights of the methodology. Later, MDE is applied to a simplified TLP model to validate the response reconstruction approach and demonstrate its applicability for TLP-like structures. Finally, a FOWT numerical model is used to design the fatigue monitoring system. The proposed system consists of two layouts of two strain gauges in the upper column of the TLP, and two layouts of two strain gauges on each pontoon. This system can provide full-field strain estimations with over 88.9% accuracy and predict fatigue damage accumulation with errors of less than 0.01%. Also, the system presented in this thesis only predicts global responses. However, the fatigue of the structure is also influenced by local structural responses due to sea pressures. Therefore, future research to include local effects in the predictions is recommended.