The new software to allow electronic voting should be available nationwide and can be used for both local and national elections, as well as referendums.
Backers of the new system say it will help stop the spread of the novel coronavirus, according to TASS, since they will no longer be required to go to polling places.
The electronic system has undergone four tests in Moscow so far and not been hacked once, the news agency reported.
Opponents have expressed misgivings, noting that an electronic system will be easier to manipulate and make it hard for independent observers to notice irregularities.
They also note that the changes are being introduced at a point in time when the pandemic means public protests are not allowed.
It is not clear whether the new system will be available for an upcoming constitutional referendum that would consolidate power under Putin and remove term limits, clearing the way for him to potentially remain in power through 2036.
The vote on the referendum had been expected in mid-April, but that date was cancelled due to the pandemic.
According to Russian media reports, the new date will likely be June 24.