Anonymity and privacy in the electoral process are mandatory features found in any democratic society, and many authors consider these fundamental civil liberties and rights. During the election process, every voter must be identified as eligible, but after casting a vote, the voter must stay anonymous, assuring voter and vote unlinkability. Voter anonymity and privacy are the most critical issues and challenges of almost all electronic voting systems. However, vote immutability must be assured as well, which is a problem in many new democracies, and Blockchain as a distributed technology meets this data immutability requirement. Our paper analyzes current solutions in Blockchain and proposes a new approach through the combination of two different Blockchains to achieve privacy and anonymity. The first Blockchain will be used for key management, while the second will store anonymous votes. The encrypted vote is salted with a nonce, hashed, and finally digitally signed with the voter’s private key, and by mixing the timestamp of votes and shuffling the order of cast votes, the chances of linking the vote to the voter will be reduced. Adopting this approach with Blockchain technology will significantly transform the current voting process by guaranteeing anonymity and privacy.