The advent of IoT has enabled the design of connected and integrated smart health monitoring systems. These smart health monitoring systems could be realized in a smart home context to render long-term care to the elderly population. In this paper, we present the design of a wearable health monitoring system suitable for older adults in a smart home context. The proposed system offers solutions to monitor the stress, blood pressure, and location of an individual within a smart home environment. The stress detection model proposed in this work uses Electrodermal Activity (EDA), Photoplethysmogram (PPG), and Skin Temperature (ST) sensors embedded in a smart wristband for detecting physiological stress. The stress detection model is trained and tested using stress labels obtained from salivary cortisol which is a clinically established biomarker for physiological stress. A voice-based prototype is also implemented and the feasibility of the proposed system for integration in a smart home environment is analyzed by simulating a data acquisition and streaming scenario. We have also proposed a blood pressure estimation model using PPG signal and advanced regression techniques for integration with the stress detection model in the wearable health monitoring system. Finally, the design of a voice-assisted indoor location system is proposed for integration with the proposed system within a smart home environment. The proposed wearable health monitoring system is an important direction to realize a smart home environment with extensive diagnostic capabilities so that such a system could be useful for rendering long-term and personalized care to the aging population in the comfort of their home.