Physical and mental well-being during the COVID-19 pandemic is typically assessed via surveys, which might make it difficult to conduct longitudinal studies and might lead to data suffering from recall bias. Ecological momentary assessment (EMA) driven smartphone apps can help alleviate such issues, allowing for in situ recordings. Implementing such an app is not trivial, necessitates strict regulatory and legal requirements, and requires short development cycles to appropriately react to abrupt changes in the pandemic. Based on an existing app framework, we developed Corona Health, an app that serves as a platform for deploying questionnaire-based studies in combination with recordings of mobile sensors. In this paper, we present the technical details of Corona Health and provide first insights into the collected data. Through collaborative efforts from experts from public health, medicine, psychology, and computer science, we released Corona Health publicly on Google Play and the Apple App Store (in July 2020) in eight languages and attracted 7290 installations so far. Currently, five studies related to physical and mental well-being are deployed and 17,241 questionnaires have been filled out. Corona Health proves to be a viable tool for conducting research related to the COVID-19 pandemic and can serve as a blueprint for future EMA-based studies. The data we collected will substantially improve our knowledge on mental and physical health states, traits and trajectories as well as its risk and protective factors over the course of the COVID-19 pandemic and its diverse prevention measures.