The increasing number of health-data breaches is creating a complicated environment for medical-data sharing and, consequently, for medical progress. Therefore, the development of new solutions that can reassure clinical sites by enabling privacy-preserving sharing of sensitive medical data in compliance with stringent regulations (e.g., HIPAA, GDPR) is now more urgent than ever. In this work, we introduce MedCo, the first operational system that enables a group of clinical sites to federate and collectively protect their data in order to share them with external investigators without worrying about security and privacy concerns. MedCo uses (a) collective homomorphic encryption to provide trust decentralization and end-to-end confidentiality protection, and (b) obfuscation techniques to achieve formal notions of privacy, such as differential privacy. A critical feature of MedCo is that it is fully integrated within the i2b2 (Informatics for Integrating Biology and the Bedside) framework, currently used in more than 300 hospitals worldwide. Therefore, it is easily adoptable by clinical sites. We demonstrate MedCo's practicality by testing it on data from The Cancer Genome Atlas in a simulated network of three institutions. Its performance is comparable to the ones of SHRINE (networked i2b2), which, in contrast, does not provide any data protection guarantee.