Under the law, signed by Putin on Saturday and passed by parliament last week, smoking will gradually be banned at work, in the subway, restaurants, cafes, ships and long-distance trains in a nation with one of the world's top smoking rates.
The legislation will also restrict cigarette sales and ban advertising and sponsorship of events by tobacco companies.
It was opposed by foreign firms such as British American Tobacco, Imperial Tobacco, Japan Tobacco, and Philip Morris, which control more than 90 percent of a Russian cigarette market worth about $20 billion annually.
Putin's aim is to force a lifestyle change on millions of Russians in a country where bars and restaurants are often filled with a thick blue haze of smoke.
But in a sign that many will resist, smokers rights' groups oppose the law and a website has sprung up which, in a nod to Russia's Communist past, declares: "Smokers of the world unite."
"I'm categorically against this stupid ban. Smoking is heavily restricted now anyway. No smoking in offices, no smoking in staircases, nowhere," said Grigory, a 60-year-old businessmen in Moscow who declined to give his second name. "I'll go out even less now as there's nowhere to go for us chain-smokers."
The law will be phased in, with smoking banned in some public places, such as subways and schools from June 1. The ban will be broadened to include restaurants and cafes a year later.
Sales of tobacco products will be forbidden at street kiosks from June 1, 2014, advertising and displaying cigarettes will be restricted, and minimum prices will be set for cigarettes which mostly cost 50 to 60 roubles for a pack of 20 (less than $2).
The law is part of Putin's drive to reverse a population decline that began after the Soviet Union collapsed in 1991. He hopes it will increase productivity and promote economic growth.
Putin has stepped up these efforts since his return to the presidency in May, mounting a campaign reminiscent of Soviet leader Mikhail Gorbachev's attempt to crack down on drinking under his failed "perestroika" reforms of the late 1980s.
Prime Minister Dmitry Medvedev said last year almost 400,000 Russians die each year from smoking-related causes. The World Bank says 40 percent of Russians smoke regularly.
World Bank figures show Russia's population slumped to 141.9 million in 2011 from 148.6 million in 1991, with average life expectancy at 69 years, against 78 in the United States. Failure to expand the workforce would limit economic growth.
Announcing Putin had signed the law, the Kremlin said on Monday it would bring Russia into line with a World Health Organization tobacco control treaty which it ratified in 2008.
Owners of the ubiquitous kiosks, which many convenience shoppers rely on, say many could go out of business, especially as they have already been hit by restriction on alcohol sales.
The All-Russian Smokers' Rights Movement said the law would not work and called instead for moves to discourage youngsters from starting smoking.
Erik Bloomquist, an analyst at Berenberg Bank, said: "In aggregate ... we do not expect the restrictions to make much difference in overall consumption or prevalence, and think the smoking bans will be honored more in the breach than in actuality."
He said increases planned in excise taxes were likely to have a bigger impact on consumption.
The move is a blow to Japan Tobacco, in which the Japanese government plans to sell about a third of its stake.
Like other tobacco companies, it said it would abide by the law but several firms said the law could increase illicit trade.
"Implementation of sales restrictions accompanied by the extensive year-on-year growth of excise in Russia may lead to a massive inflow of cheaper products from neighboring states," said Alexander Lioutyi, Corporate Affairs Director, BAT Russia.
(Additional reporting by Gabriela Baczynska and Steve Gutterman; Editing by Alistair Lyon)