The most promising way to increase voters’ confidence in the remote electronic voting (REV) procedure is a voting method based on Ethereum blockchain platform. However, the existing solutions using this method faced a range of problems: ensuring the secrecy of the vote and openness of the procedure for society, pressure on the voter and a guarantee of the reliability of the whole system. In this work, a method for constructing a REV is proposed that solves these problems. It is similar in structure to the traditional voting method, using the same principle and processes. The Ethereum blockchain based REV process is described in detail. It was shown that received votes are securely stored in the Ethereum blockchain network, and the correctness of the vote addressing to the selected candidate can always be checked in real time. The description of smart contract algorithm that implements the transfer of vote from voter to candidate using transactions and determines the winner who received the highest number of votes was provided. It was demonstrated that keccak256 hashing algorithm and secp256k1 elliptic curve signatures ensure transactions’ maximum protection, reliability, and non-rollability. The developed REV technique based on Ethereum blockchain platform increases the efficiency of data security and confidentiality, transparency and anonymity of the voting procedure, and solves the problem of coercion. The results of the work have been implemented programmatically and can be used not only in the electoral system, but also wherever there is need of remote voting.