Official results published on July 2, after 99.9% of ballots had been counted, showed that the former KGB officer who has ruled Russia 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.
That means Putin, 67, could rule until the age of 83.
The Central Election Commission said 77.9% of votes counted across the world's largest country had supported changing the constitution. Just over 21% had voted against, it said.
Ella Pamfilova, head of the commission, said the vote had been transparent and that officials had done everything to ensure its integrity.
Opposition politician Alexei Navalny had a different view and called the vote an illegitimate and illegal show designed to legalise Putin's presidency for life.
"We'll never recognise this result," Navalny told supporters in a video.
Navalny said the opposition would not protest for now because of the novel coronavirus pandemic, but would do so in big numbers in the autumn if its candidates were blocked from taking part in regional elections or their results were falsified.
"What Putin fears most is the street," said Navalny. "He... will not leave until we start to take to the streets in the hundreds of thousands and in the millions."
Russians had been encouraged to back Putin's power move, described by critics as a constitutional coup, with prize draws offering flats and an ad campaign highlighting other constitutional amendments in the same reform bundle, such as pensions protection and a de facto ban on same-sex marriages.
One-off payments of 10,000 roubles ($141) were transferred to those with children at Putin's order as people headed to polling stations on July 1, the last day of the vote, held over seven days to try to limit the spread of the virus.
Moscow resident Mikhail Volkov said he'd voted in favour of the reforms. "We need radical changes and I'm for them," he said.
'Read something and vote'
Others were less enthusiastic.
"I didn't read about the amendments if I'm honest," Lyudmila, another voter, said. "What's the point of voting if they've already decided for you. It's like that in our country - read something and vote. I voted."
Turnout was 65%, election officials said.
Putin, already the longest-serving leader in modern Russian history since Soviet dictator Josef Stalin, made no mention of how the changes could affect his own career in an eve-of-vote speech on June 30.
He has said he has yet to decide on his future. Critics, who liken Putin to a latter-day Tsar, say they are sure he will run again, but some analysts say he may want to keep his options open to avoid becoming a lame duck.
At 60%, according to the Levada pollster, his approval rating remains high but well down on its peak of nearly 90%.
With Russia reporting thousands of new COVID-19 cases each day, opponents have been unable to stage protests but have mocked the vote online, sharing photographs of polling stations in apartment stairwells, supermarket trolleys and the boot of a car.
A small group of activists staged a symbolic protest at the Red Square on July 1 afternoon, using their prostrate bodies to form the year 2036 before being swiftly detained by police, TV Rain reported.
Separately, the "No! Campaign," called on supporters to head for Moscow's Pushkinskaya Square after voting. "We need to remind the authorities that we exist and that there are tens of millions of us who do not want Putin to rule until 2036," Andrei Pivovarov, an activist, said in a video.
In the event, only dozens turned out amid a heavy police presence, a Reuters reporter said. Opposition politicians said a couple of hundred had attended. Those who did chanted "Russia will be free." Another slogan suggested Putin should resign.
Golos, a non-governmental organization that monitors elections, cited numerous irregularities with the vote and said it would not be able to confirm the outcome as legitimate.
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