Disseminating medical data beyond the protected cloud of institutions poses severe risks to patients' privacy, as breaches push them to the point where they abstain from full disclosure of their condition. This situation negatively impacts the patient, scientific research, and all stakeholders. To address this challenge, we propose a blockchain-based data sharing framework that sufficiently addresses the access control challenges associated with sensitive data stored in the cloud using immutability and built-in autonomy properties of the blockchain. Our system is based on a permissioned blockchain which allows access to only invited, and hence verified users. As a result of this design, further accountability is guaranteed as all users are already known and a log of their actions is kept by the blockchain. The system permits users to request data from the shared pool after their identities and cryptographic keys are verified. The evidence from the system evaluation shows that our scheme is lightweight, scalable, and efficient.