The Internet of Things (IoT) is an emerging network paradigm that can connect anyone and anything at any time and any place within any network. For long-term IoT-connected health monitoring applications, different solar energy harvesting techniques are investigated for both wearable and implantable biomedical sensors in this thesis. In addition, a compact wearable sensor patch in a rigid-flex design is proposed for real-time vital signs monitoring remotely. A Bluetooth Low Energy (BLE) module is employed to transmit physiological signals to a gateway, which will forward health data to the Internet cloud for future IoT-connected healthcare applications.