Medical Internet of Things (IoT) solutions are already paving the way towards the realization of Smart Hospitals. Following this trend, we propose an IoT cloud-based network for anesthesia on-line monitoring. This architecture allows the anesthesiologist to remain simultaneously connected to all the patients under his/her responsibility. To do so, the Android app, running on the anesthesiologists tablet/smartphone, plays the central role of the architecture. From one side, it receives data from the Therapeutic Drug Monitoring (TDM) system on the patient; on the other side, it pushes data to the cloud, exploiting the Pryv middleware solution, enabling teleconsulting. All the communications exploits Wi-Fi, therefore, all data are also stored locally in the physical devices's memory to face Internet unavailability. The flexibility and the portability of our monitoring architecture ensure the possibility to interface with any medical device which can wirelessly send the measured data. Therefore, a variety of medical monitoring applications can also be addressed.