The amendments, proposed by Medvedev during his first state of the nation address in early November, were approved by the lower and upper houses of parliament later that month.
Medvedev's proposal triggered speculation that the extension of the terms, which will apply to the next head of state and legislature, was a pretext for the return to office of his predecessor, Prime Minister Vladimir Putin.
Earlier this month, all of Russia's 83 regions approved the constitutional amendments. Under the Constitution, the approval of at least two-thirds of regional legislatures was required to extend the current four-year presidential and parliamentary terms.
The amendments also envision the submission of annual government reports to parliament.
The State Duma, the lower house, will be authorized to consider governmental reports on its activity and demand answers to questions raised by lawmakers.
The amendments come into force after they are signed by the president and published in a government newspaper.
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Russia has become very adept in playing the diplomatic game, in which victory depends on choosing the right associate or partner. But there are a growing number of claimants to this role in the new horizontal and interdependent world. Aside Syria and Iran, being still important, the new venues for the application of practical diplomacy may well be Ukraine, the East China Sea and Afghanistan.