Many recent research efforts have focused on developing high-performance wearable health monitoring systems. This work presents a mechanically stretchable and skin-mountable sensor system based on a conductive polymer composite-based elastic printed circuit board (EPCB) in which a resistive-type composite strain sensor is monolithically integrated. The composite-based EPCB is simply prepared by patterning a silver nanowire (AgNW)/dragon skin (AgNW/DS) composite film in a programmable manner using a direct cut patterning technique. The proposed sensor system was successfully fabricated by directly mounting various components (e.g., microcontroller, circuit elements, light emitting device chips, temperature sensor, Bluetooth module) on the prepared AgNW/DS-based EPCB. The fabricated sensor system was found to be highly stretchable and rollable enough to maintain tight adhesion to the wrist region without significant physical deterioration, even when the wrist was in motion. The wireless sensor system attached to the wrist part enabled us to monitor the wrist motion and surrounding temperature in real time, opening the possible application as a wearable health monitoring platform.