Falls are a main cause of injury for patients with certain diseases. Patients who wear health monitoring systems can go about daily activities without limitations, thereby enhancing their quality of life. In this paper, patient falls and heart rate were accurately detected and measured using two proposed algorithms. The first algorithm, abnormal heart rate detection (AHRD), improves patient heart rate measurement accuracy and distinguishes between normal and abnormal heart rate functions. The second algorithm, TB-AIC, combines an acceleration threshold and monitoring of patient activity/inactivity functions to accurately detect patient falls. The two algorithms were practically implemented in a proposed autonomous wireless health monitoring system (AWHMS). The AWHMS was implemented based on a GSM module, GPS, microcontroller, heartbeat and accelerometer sensors, and a smartphone. The measurement accuracy of the recorded heart rate was evaluated based on the mean absolute error, Bland–Altman plots, and correlation coefficients. Fourteen types of patient activities were considered (seven types of falling and seven types of daily activities) to determine the fall detection accuracy. The results indicate that the proposed AWHMS succeeded in monitoring the patient’s vital signs, with heart rate measurement and fall detection accuracies of 98.75% and 99.11%, respectively. In addition, the sensitivity and specificity of the fall detection algorithm (both 99.12%) were explored.