This paper presents a non-contact vital signs (respiration and heartbeat) monitoring system that utilizes visible light sensing (VLS) technology. We have for the first time demonstrated the ability to wirelessly (non-contact) sense vital signs using only reflected incoherent light signals from a human subject. The VLS-based system is implemented by using simple visible light source, photodetector and data acquisition/processing unit, and is used with the developed signal processing algorithms to turn slight variations in reflected light power into accurate measurements of respiration and heart rate. To assess the accuracy of our method, the results were compared with reliable measurements using a contact-based monitoring device (ground truth). More than 94% of accuracy was observed in test results including both breathing and heartbeat rates in different scenarios as compared to the state-of-the-art baseline methods such as contact-based vitals monitoring devices. These competitive results have demonstrated that VLS-based vitals monitoring innovation is indeed a viable, powerful, attractive, low-cost and safe method. This study represents a substantive departure from the traditional ways of doing non-contact vitals monitoring methods (e.g., radio-frequency-based radars and imaging-based cameras) and is poised to make big contributions to this area. Since vital signs monitoring is a ubiquitous element of medicine, this work would also impact the entire health care community, from patients in their homes, to doctor's offices, to large medical institutions and industries. This technology has potential to address numerous conditions and situations in which vital signs are critical indicators such as sleep apnea and human-computer-interaction applications.