In the traditional medical healthcare system, each medical facility is responsible for preserving its own records. Sharing such records with another medical establishment is difficult for them. To tackle this challenge, the traditional medical system leverages internet technology to transform into a modern electronic system. In electronic healthcare systems, managing the security and privacy of patient data becomes a major issue. As an alternative, the healthcare sector might use blockchain technology to exchange digitised healthcare data. Blockchain technology is characterised by anonymity, decentralisation, and immutability. It is hard to keep all electronic healthcare data on blockchain due to the expense and volume. Cloud computing is the best solution for storing this type of data and resolving problems like these. To address these concerns, we offer a blockchain-based key agreement protocol for cloud medical network systems that enhances privacy and security. We demonstrate a formal and informal security analysis of the proposed protocol that shows that the proposed protocol is both secure and communicative. We provide security verification of the proposed protocol by using the AVISPA software tool against man in the middle attack and replay attack. Finally, we compute the computation and communication costs of the proposed protocol and other existing protocols, the proposed protocol has less computation and communication costs than other existing protocols in the electronic healthcare system.