The State Duma adopted final amendments to the bill, which frees thousands of Russians, mainly juveniles, invalids, veterans, pregnant women and women with children.
The amnesty was extended to suspects of hooliganism, which means that charges against 30 people abroad the Greenpeace ship who were held after an oil rig protest in Russia's Arctic 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 on charges of hooliganism for an impromptu protest at Moscow's main cathedral.
Pyotr Verzilov, Tolokonnikova's husband, said he expected she could be freed imminently.
The proposed amnesty would also set free and drop the charges against at least eight defendants in the Bolotnaya case where 26 people are either on trial or were charged in connection to a 2012 protest rally on the Bolotnaya square in Moscow which ended in scuffles between protesters and riot police.