eHealth systems provide medical support to users and contribute to the development of mobile and quality health care. They also provide results on the prevention and follow-up of diseases by monitoring health-status indicators and methodical data gathering in patients. Telematic management of health services by means of the Internet of Things provides immediate support and it is cheaper than conventional physical presence methods. Currently, wireless communications and sensor networks allow a person or group to be monitored remotely. The aim of this paper is to develop and assess a system for monitoring physiological parameters to be applied in different scenarios, such as health or sports. This system is based on a distributed architecture, where physiological data of a person are collected by several sensors; next, a Raspberry Pi joins the information and makes a standardization process; then, these data are sent to the Cloud to be processed. Our Cloud system stores the received data and makes a data fusion process in order to indicate the athlete's fatigue status at every moment. This system has been tested in collaboration with a small group of voluntary tri-athletes. A network simulation has been performed to plan a monitoring network for a bigger group of athletes. Finally, we have found that this system is useful for medium-term monitoring of the sports activities