In 2019, a new virus, SARS-CoV-2, responsible for the COVID-19 disease, was discovered. Asymptomatic and mildly symptomatic patients were forced to quarantine and closely monitor their symptoms and vital signs, most of the time at home. This paper describes e-CoVig, a novel mHealth application, developed as an alternative to the current monitoring paradigm, where the patients are followed up by ... [Show full abstract] direct phone contact. The e-CoVig provides a set of functionalities for remote reporting of symptoms, vital signs, and other clinical information to the health services taking care of these patients. The application is designed to register and transmit the heart rate, blood oxygen saturation (SpO2), body temperature, respiration, and cough. The system features a mobile application, a web/cloud platform, and a low-cost specific device to acquire the temperature and SpO2. The architecture of the system is flexible and can be configured for different operation conditions. Current commercial devices, such as oximeters and thermometers, can also be used and read using the optical character recognition (OCR) functionality of the system. The data acquired at the mobile application are sent automatically to the web/cloud application and made available in real-time to the medical staff, enabling the follow-up of several users simultaneously without the need for time consuming phone call interactions. The system was already tested for its feasibility and a preliminary deployment was performed on a nursing home showing promising results.