The 47-member Council of Europe, which includes Russia, is an international body set up to promote democracy, protect human rights and the rule of law on the continent.
Russia was the only country on the council that had refused to ratify Protocol 14 to the European rights convention, preventing it from coming into force.
The protocol gives the council's committee of ministers the power to bring a member state before the Strasbourg-based European Court of Human Rights for non-compliance with a previous judgment against that state.
It also reduces the number of judges on panels charged with deciding issues such as the admissibility of cases.
Some pro-Kremlin politicians feared passing the protocol could put pressure on Russia, which faces the largest number of cases pending before the court.
But Medvedev said at a meeting with officials last month that consultations with the court and the council had helped assuage some of the Russian concerns about the new rules of the court's operations.
He also said that Russia was interested in helping to making the court more efficient.
Russia's reluctance so far has reflected its irritation over the court's many rulings that found the country at fault in scores of cases filed related to abductions and killings in Chechnya and rights abuses in other Russian regions.
Human Rights Watch said last September that Moscow ignored more than 100 of the court's rulings, which found Russian authorities responsible for killings, abductions and torture.
Andrei Denisov, Russia's deputy foreign minister, told politicians on Friday that the country had received assurances that its representative in the court will be invited to sit in hearings of appeals filed by Russians.
He also said that the council's decision-making body will consult with Russia on how to enforce the court's rulings.
Denisov argued that the document's ratification is key to improving Russia's ties with European nations, some of which accused Moscow of hampering the court's work by failing to endorse its reform.
The Communists were the only Duma faction which voted against the document.
Sergei Reshulsky, a Communist politician, warned that the new rules covering the court's operation would raise the heat on Russia despite official's assurances.