The healthcare industry faces challenges due to rising treatment costs, an aging population, and limited medical resources. Remote monitoring technology offers a promising solution to these issues. This paper introduces an innovative adaptive method that deploys an Ultra-Wideband (UWB) radar-based Internet-of-Medical-Things (IoMT) system to remotely monitor elderly individuals’ vital signs and fall events during their daily routines. The system employs edge computing for prioritizing critical tasks and a combined cloud infrastructure for further processing and storage. This approach enables monitoring and telehealth services for elderly individuals. A case study demonstrates the system’s effectiveness in accurately recognizing high-risk conditions and abnormal activities such as sleep apnea and falls. The experimental results show that the proposed system achieved high accuracy levels, with a Mean Absolute Error (MAE) ± Standard Deviation of Absolute Error (SDAE) of 1.23±1.16 bpm for heart rate (HR) detection and 0.22±0.27 bpm for respiratory rate (RR) detection. Moreover, the system demonstrated a recognition accuracy of 90.60% for three types of falls (i.e., stand, bow, squat to fall), one daily activity, and No Activity Background. These findings indicate that the radar sensor provides a high degree of accuracy suitable for various remote monitoring applications, thus enhancing the safety and well-being of elderly individuals in their homes.