But it wasn't immediately clear when or if the 30 Greenpeace activists, including two Canadians, would be allowed to leave the country.
Paul Ruzycki of Port Colborne, Ont., and Alexandre Paul of Montreal were granted bail by a Russian court last month.<
The amnesty has been largely viewed as the Kremlin's attempt to soothe criticism of Russia's human rights records ahead of the Winter Olympics in Sochi next year.
Opposition lawmakers argued it doesn't go nearly far enough and the complicated legislation appeared to leave many questions open.
Greenpeace said in a statement that the activists, who spent two months in jail after being arrested during a protest at a Russian oil rig in the Arctic, are relieved to hear news of the amnesty but added: “There is no amnesty for the Arctic.”
The State Duma on Wednesday voted 446-0 in favour of the carefully tailored bill, which mainly concerns those who haven't committed violent crimes, first-time offenders, minors and women with small children.
Lawmakers said they expect about 2,000 people to be released from jail.
The Duma adopted last-minute final amendments to the bill to include suspects of hooliganism who are still awaiting trial, which means that charges against the people aboard a Greenpeace ship who were detained after a protest in September are likely to be dropped.
The bill is also expected to release Nadezhda Tolokonnikova and Maria Alekhina, the jailed members of the Pussy Riot punk band who are serving two years in prison on charges of hooliganism for an irreverent protest at Moscow's main cathedral.
But it was still unclear on Wednesday whether the Greenpeace crew members could face new charges not covered by the amnesty. They were initially accused of piracy but authorities later changed that charge to hooliganism.
The Investigative Committee has insisted the probe into the incident isn't over yet and that some of the crew members could face additional charges, such as assaulting a law enforcement official.
The amnesty does not cover former oil tycoon Mikhail Khodorkovsky, who has been widely described as Russia's main political prisoner, and only eight out of 26 defendants who took part in a 2012 protest rally on the Bolotnaya square in Moscow that ended in scuffles between protesters and riot police.
Opposition lawmaker Dmitry Gudkov said the amnesty bill "has buried all hopes of human rights activists and families of political prisoners that their children and family members will be set free."
The amnesty will go into effect as soon as the bill is published in the government newspaper, which is expected to happen on Thursday. But it allows prosecutors a six-month period to carry it out, meaning some of the prisoners could in theory wait weeks or months before getting released. Prisoners would apply to prison administration for amnesty, and prosecutors would decide whether they were eligible.
Lawyers and families of the Pussy Riot members insist that everyone eligible for the release ought to be allowed to walk free as soon as the bill is published. The two are now slated to be released in March.
Pyotr Verzilov, Tolokonnikova's husband, told The Associated Press he believes there is nothing to stop his wife from being released if the bill is published on Thursday.
Greenpeace said in a statement it hopes that the amnesty bill will allow foreign crew members of the Arctic ship to get exit visas and leave Russia. The crew members insist the charges against them were bogus.
"I might soon be going home to my family, but I should never have been charged and jailed in the first place," the ship's captain Peter Willcox said in the statement.
— With files from The Canadian Press