The spread of informatics and electronic systems capable of the real-time monitoring of multiple psychophysiological signals has continuously grown in the last few years. In this study, we propose a novel open-source wearable monitoring platform (WMP) to synchronously acquire and process multiple physiological signals in a real-time fashion. Specifically, we developed an IoT-like modular and fully open-source platform composed of two main blocks that on the one hand connect multiple devices (the sensor fusion unit) and on the other hand process and store the sensors’ data through the internet (the remote storing and processing unit). To test the proposed platform and its computational performance, 15 subjects underwent an experimental protocol, in which they were exposed to rest and stressful sessions implementing the Stroop Color and Word Test (SCWT). Statistical analysis was performed to verify whether the WMP could monitor the expected variations in the subjects’ psychophysiological state induced by the SCWT. The WMP showed very good computational performance for data streaming, remote storing, and real-time processing. Moreover, the experimental results showed that the platform was reliable when capturing physiological changes coherently with the emotional salience of the SCWT.