Prime Minister Dmitry Medvedev, the President's political sidekick, will also be stepping down and taking up a newly-created back seat role in defence.
Putin thanked members of the government for their work but added that "not everything worked out".
The dramatic moves were widely seen as preparing the ground for 2024, when Putin, now 67, is constitutionally obliged to leave the presidency after occupying the Kremlin or the prime minister's job continuously since 1999.
At the same time, Putin said Russian Federation must remain a "strong presidential republic", with the president retaining powers such as the right to dismiss the prime minister and cabinet ministers, as well as naming top defense and security officials.
He is ending his term as president, and the objective of yesterday's message is amendments to the Constitution, which now, when president may not be Putin, take away all power from that president, transfer it him to another post. The president should retain the right to dismiss the prime minister and Cabinet ministers, to name top defence and security officials, and to be in charge of the Russian military and law enforcement agencies, he said.
In his speech, Putin said the changes would help Russia's parliament take more responsibility in policymaking.
Russia's opposition also said the proposals indicate Putin's desire to stay in power. However, there is nothing stopping him from becoming prime minister, as he did in 2008, when he and Medvedev swapped roles for four years.
He suggested that a clause limiting the president to two successive terms could be changed, but did not specify how.
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But the 53-year-old Mishustin, the longtime chief of Russia's tax service, was tapped for the post by President Vladimir Putin. Such a model resembling the Chinese one would allow Putin to stay at the helm indefinitely while encouraging rivalry between potential successors, Rogov said on Facebook.
In addition, he also talked about a constitutional change that would enshrine the priority of domestic legislation over worldwide law.
"People should already now be feeling real changes for the better", Mr Mishustin said.
"I don't know how it will be called - chairman of the State Council, prime minister, or something like what happened in Kazakhstan, but it will be one person - Putin", he said.
Putin named Mikhail Mishustin, Russia's head of tax service as a replacement for Medvedev.
But also relevant is power politics. Russia's population now stands at about 147 million. United Russia, the ruling party, has a majority in the Duma, meaning Mishustin's confirmation, barring an unexpected upset, is assured.
Among other things, Putin proposed approving priority of the Constitution over global treaties.
The last referendum was held in 1993 to ratify the Constitution of Boris Yeltsin, Putin's predecessor.
Mishustin vowed to focus on social issues and improve living standards. He promised that the government would offer additional subsidies to families that have children.