Source: Pool Sputnik Kremlin
Other amendments would strengthen presidential and parliamentary powers, enshrine traditional values including an effective ban on gay marriage and guarantee better minimum wages and pensions.
Russia's two houses of parliament previously approved the amendments but Mr Putin said they would only take effect if supported by a majority of voters.
Leading Kremlin critic Alexei Navalny described early results showing Russians' strong backing for the reforms as a "huge lie" that didn't reflect reality.
'Stability, security, prosperity'
In a final appeal to voters on Tuesday, Mr Putin said the changes were needed to ensure Russia's future "stability, security, prosperity".
State television showed Mr Putin voting Wednesday at his usual polling station at the Russian Academy of Sciences, where he was handed a ballot by an electoral worker wearing a surgical mask and gloves.
Dressed in a dark suit and tie, Putin was not wearing any protective gear.
At a polling station in Vladivostok in Russia's far east, 79-year-old Valentina Kungurtseva told AFP she supported the reforms.
"For us as pensioners, it's very important that they will increase our pension every year," she said.
"As long as we have a good president, life will be good."
In the second city, Saint Petersburg, 20-year-old Sergei Goritsvetov said he opposed the reforms but doubted it would make any difference.
"I voted against and I hope there will be many of us, but I don't know what it will change," he said. "At least I expressed my opinion."
Mr Navalny had said Mr Putin, 67 and in power as president or prime minister since 2000, wants to make himself "president for life" and called for a boycott, calling the vote illegitimate.
"We have just watched a show with a planned finale," he wrote on his blog after polls closed.
"Putin will not leave himself," Mr Navalny wrote, "not until we begin to come out to the streets by the hundreds of thousands, by millions."
The opposition divided and failed to mount a serious campaign, with some voting "no" and others staying home. There were only small protests in central Moscow and Saint-Petersburg Wednesday.
Falling approval ratings
Golos, an independent election monitor, said it had received hundreds of complaints of violations, including people voting more than once and claims employers were putting pressure on staff to cast ballots.
Election commission chief Ella Pamfilova denied any problems on Wednesday, saying only a couple of violations were confirmed and they would have no effect on the result.
Mr Putin's approval rating has fallen in recent months. It stood at 60 per cent in June according to pollster Levada, down 20 points from the months after his re-election in 2018.
Analysts say Mr Putin wanted to get the vote over with before Russians, already suffering from several years of falling incomes, are hit by the full economic impact of the pandemic.
Mr Putin said in a recent interview that he had not decided whether to run again but suggested that part of the reason for the presidential reset was to allow Russia's political elite to focus on governing instead of "hunting for possible successors".