The sum of Big Data generated from different sources is increasing significantly with each passing day to extent that it is becoming challenging for traditional storage methods to store this massive amount of data. For this reason, most organizations have resolved to use third-party cloud storage to store data. Cloud storage has advanced in recent times, but it still faces numerous challenges with regard to security and privacy. This paper discusses Big Data security and privacy challenges and the minimum requirements that must be provided by future solutions. The main objective of this paper is to propose a new technical framework to control and manage Big Data security and privacy risks. A design science research methodology is used to carry out this project. The proposed framework takes advantage of Blockchain technology to provide secure storage of Big Data by managing its metadata and policies and eliminating external parties to maintain data security and privacy. Additionally, it uses mobile agent technology to take advantage of the benefits related to system performance in general. We present a prototype implementation for our proposed framework using the Ethereum Blockchain in a real data storage scenario. The empirical results and framework evaluation show that our proposed framework provides an effective solution for secure data storage in a Big Data environment.