Structure Health Monitoring provides a solution for damage detection, identification and monitoring the structural behavior through collection of data from several points on the structure. In this work, we present the design and operation of an Internet of Things based structural health monitoring system. The vibration signals are collected from specific points from the monitored structure using a processing node with wireless internet connectivity. Then, the sensors data are grouped and transmitted via cellular network to a remote server where an appropriate damage detection algorithm is applied on the collected data to assess the status of the structure. We provide details about the proposed systems design and operation including the hardware and software parts. Moreover, we augment the study with a practical experiment in which a five-story building was tested under healthy and damaged status. The results show the feasibility of the proposed system in automating the damage detection process.