Recently, Electronic Health Records (EHR) plays a significant role in E-health care system that allows data exchange of patient's health records via a portal designated by healthcare professionals. In this, the lack of confidentiality and integrity factors leads to different security issues on sensitive health information and causes a serious impact on a patient's life. To accomplish the security of medical data, we propose a new scheme named Elliptical Curve Certificateless Aggregate Cryptography Signature scheme (EC-ACS) for the public verification and auditing in the Medical Cloud Server (MCS) to secure EHR using authorized blockchain technology. In this, we use Elliptic Curve Cryptography (ECC) to encrypt medical data and the Certificateless Aggregate Signature scheme (CAS) to generate the digital signature for sharing and storing data in the cloud storage. This proposed scheme ensures security, privacy and safeguards the confidential information from unauthorized access in the cloud health system. Furthermore, the blockchain technique guarantees the integrity, traceability and secure storage of medical records in the cloud environment.