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In this paper, we present the development of a polymer optical fiber (POF) sensor for simultaneous measurement of breath (BR) and heart rates (HR). The sensor is embedded as a smart textile solution that can be used within the user’s clothes. In addition, a signal processing technique is proposed for obtaining the HR and BR without the influence of body movements and in different positions of the user’s chest. Sensor signal processing and analysis are made in the frequency domain and different filters are applied. Results show errors below 4 beats per minute and 2 breaths per minute for the HR and BR, respectively, even when the user is performing periodic body movements such as the ones induced by the gait. Thus, the proposed POF-based smart textile is a low-cost solution with good accuracy that can be readily applied in the remote monitoring of patients at home without disturbing their daily activities.