Medvedev's final endorsement of the legislation follows its quick approval by the Kremlin-controlled parliament and all of Russia's 83 provincial legislatures. The change won't apply to Medvedev's current term, due to end in 2012.
Putin was barred constitutionally from seeking a third straight term as president. He tapped Medvedev, his longtime protege, as his favored successor, ensuring a landslide victory in a March election.
Putin then became prime minister and leader of the United Russia party, which dominates the parliament.
Putin remains popular and is still seen as the man calling the shots in Russia. But the rush to amend the constitution just months after Medvedev's election has led to speculation that Putin wants to return to office now — before the financial crisis erodes his popularity.
Most analysts expect Medvedev would step aside if Putin asked him to do so. But some think the president could try to strengthen his position at Putin's expense as Russians become increasingly angry over economic difficulties.
Medvedev appeared to issue a veiled criticism of his mentor's course Monday, when he said that the Cabinet's anti-crisis program was "well-balanced but not ideal."
The president quickly toned down his criticism by saying that "no ideal programs exist," but some saw it as a rare, visible crack in the Putin-Medvedev tandem.
"Medvedev may wait until Putin loses his popularity as the economy worsens by the day and dismiss him," independent political analyst Dmitry Oreshkin was quoted by online Gazeta.ru as saying.
Medvedev also turned his attention Tuesday to foreign affairs, once again expressing hope that that Russia and the United States could mend ties frayed by disputes over U.S. missile defense plans and Russia's war in Georgia in August.
In a New Year's wish to President-elect Barack Obama, Medvedev suggested the two nations could expand their cooperation on the basis of "pragmatism and a balance of interests."
Excerpts of Medvedev's telegram to Obama were released by the Kremlin.