In recent years, Global Navigation Satellite System (GNSS) technologies, which take full advantage of both real-time kinematic (RTK) and precise point positioning (PPP), managed to reach centimeter-level positioning accuracy with ambiguity resolution (AR) quick convergence techniques. One great advantage over traditional structural health monitoring (SHM) systems is that GNSS technologies will be functional in disaster management situations, when terrestrial communication links become unavailable. In this study, a multi-GNSS system, based on GPS and Galileo constellations and exploiting advanced RTK and PPP-AR technologies with update rate of 100 Hz is tested on two benchmark structures as an SHM system. The first case study served as a baseline to outline the methodology: first, a setup phase of the instrumentation, then a signal processing phase and last, the validation of the results. The methodology was then applied to a real-case scenario, in which the GNSS was tested on a road bridge. A comparative analysis with the results acquired by a set of accelerometers showed that the GNSS was able to identify the crossing of heavy vehicles. The work is paving the way for the development of an affordable and efficient multi-GNSS-based tool for the monitoring of civil infrastructures.