Two women from the Russian punk protest band Pussy Riot could also be released after Parliament unanimously passed an amnesty bill yesterday.
The amnesty specifically relates to those accused of hooliganism.
The reprieve is widely viewed as the Kremlin's attempt to soothe criticism of Russia's human rights record ahead of the Winter Olympics in Sochi in February, though it will come too late to prevent a boycott of the Games by several heads of state.
Ruling party MPs said the amnesty would free up to 3500 people in all. It is expected to go into effect as soon as the bill is published in the government gazette today, but the wording allows prosecutors a six-month enactment period, meaning some prisoners could wait months before being released.
Pyotr Verzilov, the husband of Nadezhda Tolokonnikova, one of the two jailed members of Pussy Riot, said there would be nothing to stop his wife being released if the bill was published on schedule.
Tolokonnikova received a two-year sentence, which ends in March, with Maria Alekhina, for staging an anti-Putin "punk prayer" protest at Moscow's main cathedral in February last year.
US President Barack Obama will boycott the Winter Olympics in Sochi but will send two openly gay sports stars in his place in a pointed message to Russia amid a furore over a law targeting homosexuality.
The American delegation will include tennis champion Billie Jean King, 70, and Caitlin Cahow, an ice hockey player and 2010 Olympic Winter Games silver medallist, who is also public about her sexuality.
Neither the President nor the Vice-President would attend the opening or closing ceremonies.
Russia's adoption in June of a law prohibiting the dissemination of information about homosexuality to minors has prompted protests from international human rights groups as well as calls for a boycott of the country's first post-Soviet Games. The presidents of France and Germany have already said that they would not attend.