Wearable intelligent health monitoring devices with on-device biomedical AI processor can be used to detect the abnormity in users' biomedical signals (e.g., ECG arrythmia classification, EEG-based seizure detection). This requires ultra-low power and reconfigurable biomedical AI processor to support battery-supplied wearable devices and versatile intelligent health monitoring applications while achieving high classification accuracy. However, existing designs have issues in meeting one or more of the above requirements. In this work, a reconfigurable biomedical AI processor (named BioAIP) is proposed, mainly featuring: 1) a reconfigurable biomedical AI processing architecture to support versatile biomedical AI processing. 2) an event-driven biomedical AI processing architecture with approximate data compression to reduce the power consumption. 3) an AI-based adaptive-learning architecture to address patient-to-patient variation and improve the classification accuracy. The design has been implemented and fabricated using a 65nm CMOS process technology. It has been demonstrated with three typical biomedical AI applications, including ECG arrythmia classification, EEG-based seizure detection and EMG-based hand gesture recognition. Compared with the state-of-the-art designs optimized for single biomedical AI tasks, the BioAIP achieves the lowest energy per classification among the designs with similar accuracy, while supporting various biomedical AI tasks.