Voters in Estonia totaled 7,526, of whom 6,747, or 89.65 percent, were in favor of the constitutional reforms, while 733, or 9.74 percent, were against.
Official results published on Thursday, after 99.9 per cent of ballots had been counted, showed that the former KGB officer, who has ruled Russian Federation for more than two decades as President or Prime Minister, had easily won the right to run for two more six-year terms after the current one ends in 2024.
Russia's Central Elections Commission announced early Thursday that almost 78 percent of voters had cast their ballot in favour of the changes to the constitution that could see Putin, 67, remain in power until 2036.
The vote, which was originally scheduled for April 22, had to be postponed after health officials reported a spike in coronavirus cases that overwhelmed hospitals and saw Russian Federation become the world's most infected country after the United States and Brazil.
A Russian woman living in Israel reported that she'd been able to vote three times - in Tel Aviv, in Haifa, and again online.
Chinese Foreign Ministry spokesperson Zhao Lijian said on Thursday that the results of the vote have indicated the choice of the Russian people.
Putin's approval rating was at 59% in May, according to the Levada Center, Russia's top independent pollster.
Other amendments strengthen presidential and parliamentary powers, enshrine traditional values including an effective ban on gay marriage and guarantee better minimum wages and pensions.
Asked if he might stay in power that long, Putin - the country's ruler for two decades, alternating as president or prime minister - said that "he did not exclude anything", citing the need to maintain political stability.
Russia's two houses of parliament previously approved the amendments but Putin said they would only take effect if supported by a majority of voters.
"We are voting for the country. we want to pass on to our children and grandchildren", Putin said on Tuesday.
To lure crowds to the ballot, the last day of voting was declared a national holiday and prizes - including apartments, cars and cash - were on offer to voters.
But opposition politician Alexei Navalny had a different view and described the vote an illegitimate and illegal show purely created to legalise Mr Putin's presidency for life.
Russian President Vladimir Putin on Friday mocked a rainbow LGBT pride flag hung from the U.S. embassy in Moscow, suggesting it reflected the sexual orientation of the diplomats.
The opposition divided and failed to mount a serious campaign, with some voting "no" and others staying home.
Opponents of the amendments said they planned to protest against the results in Moscow's Pushkin Square.
Golos, an independent election monitor, said it had received hundreds of complaints of violations, including people voting a few times and claims employers were putting pressure on staff to cast ballots.
"What Putin fears most is the street", Mr Navalny added.
Election commission chief Ella Pamfilova rebuffed the criticisms, saying that "there is no doubt that the vote is valid and legitimate". "They come into force, without overstating it, at the people's will", Putin said after he signed a decree to have the constitution revised.
The president said in an interview on state-run TV in June that he didn't rule out the possibility of running for office again if the Constitution were to be revised.