The lack of precise and comprehensive information about the health of bridges, and in particular long span ones, can lead to incorrect decisions regarding maintenance, repair, modernization, and reinforcement of the structure itself. While the consequences of inadequate interventions are quite apparent, incorrect decisions can also result in unnecessary or misdirected actions. For example, an inadequate assessment of the structural health can lead to the modernization and replacement of some components that are still sound. Structural Health Monitoring (SHM) involves the use of time series derived from periodic measurements of the structure’s behavior, considered in its operational and load environment. The goal is to determine its response to various solicitations and, in particular, to highlight any critical issue in the structure’s behavior that may affect its reliability and safety due to anomalies and deterioration. This paper proposes an SHM method applied to the Valgadena bridge, one of the tallest viaducts in Italy and Europe (maximum height 160 m), located on the Altopiano dei Sette Comuni in the Province of Vicenza. Despite the fact that the viaduct itself had already been monitored during its construction using classical geometric leveling techniques, the methodology proposed here is based instead on the use of affordable dual-frequency GNSS (Global Navigation Satellite System) receivers to determine static and dynamic components of the bridge movements. Specifically, an effective combination of time series analysis methods and machine learning techniques is proposed in order to determine the vibration modes of the monitored viaduct. Monitoring is performed in regular operation conditions of the bridge (operational modal analysis (OMA)), and the use of certain machine learning methods aims at supporting the development of an effective automatic OMA procedure. To be more specific, the random decrements technique is used in order to make the vibration characteristics of the collected signals more apparent. Time-domain-based subspace identification is applied in order to determine a proper model of the collected measurements. Then, clustering methods, namely DBSCAN (Density-Based Spatial Clustering of Applications with Noise) and GMMs (Gaussian Mixture Models), are used in order to reliably estimate the system poles, and hence the corresponding vibration characteristics. The performance of the considered methods is compared on the Valgadena bridge case study, showing that the use of GMM clustering reduces, with respect to DBSCAN, the impact of the choice of certain parameter values in the considered case.