Measurements of vital signs and behavioral patterns can be translated into accurate predictors of health risk, even at an early stage, and can be combined with alarm-triggering systems in order to initiate the appropriate actions. The paper presents the design and implementation of a mobile TeleCare system based on a smart wrist-worn device with a non-obtrusive sensing module for cardiac, respiratory and motor activity, a microcontroller platform for primary processing of the data from the sensors and wireless communication using Bluetooth protocol. Advanced data processing, data management, human computing interfacing and data communication are implemented using a smartphone running Android operating system (OS). A Web based health TeleCare information system was implemented being characterized by the following functionalities: data synchronization with the smartphone, advanced data processing and data presentation assuring a comprehensive data analysis and evidence based health management as well as for remote assistance of the patients by doctors and nurses. Experimental results associated with vital signs sensing and the software implementation are included in the paper.