While Putin continued calling the shots during Medvedev's presidency, he wasn't quite happy with his performance.
Putin reportedly thanked Medvedev's government for its work.
Putin also said he plans to create a position of deputy secretary of Russia's security council, and offer it to Medvedev, Russia's RT TV channel reported.
The surprise announcement came after Putin proposed constitutional amendments that would strengthen the powers of the prime minister and parliament at the expense of the presidency.
Medvedev's decision to step down after one term to let Putin return to the presidency also sparked massive protests in Moscow in 2011-2012 in a major challenge to the Kremlin.
"I propose. entrusting the State Duma with the power to approve the candidacy of the Prime Minister, and then, per the prime minister's proposal, [appoint] all deputy prime ministers and federal ministers".
Akimenko agreed that this sort of role could play in Putin's favor: "The State Council's future role is now undefined, but it could be an arbitrator, meaning that when there is a dispute, the State Council could have a final say". The authority to make those appointments now belongs to Russia's president.
Speaking to BBC's Today programme, former Prime Minister Mikhail Kasyanov said the President could be eyeing on running "forever".
A nationwide referendum would be conducted to confirm the changes, Putin said. Medvedev stepped down in 2012 when Putin became president and took up the role of PM.
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But Putin has suggested this time he will not repeat the trick and on Wednesday suggested that the word "consecutive" be removed from the constitutional article on term limits.
"Such a model resembling the Chinese one would allow Putin to stay at the helm indefinitely while encouraging rivalry between potential successors", Rogov observed.
The Russian president said changes to the constitution will be put up to a national vote soon.
Mishustin's lack of political ambition or any political experience indicates that he is likely to dutifully carry out the Kremlin's wishes as the head of the Cabinet - which some commentators point out is especially important in the "transition period" of constitutional reforms proposed by Putin.
Sergey Utkin, the head of strategic analysis at the Moscow-based Primakov Institute of World Economy and International Relations, said that it wasn't yet clear whether Mr. Putin meant to return to the Prime Minister's job again in 2024.
After the departure of his long-serving prime minister Wednesday, Russian authorities moved quickly Thursday to make Putin's vision a reality, with a confirmation vote scheduled for later in the day, as well as a meeting of the group that will draft the constitutional changes.
Although not active in politics, he has rubbed shoulders or even collided with politicians as a player in the amateur Night Hockey League, in which Putin also plays. He has won a good reputation among experts who praised him for boosting tax collection and streamlining Russia's rigid tax administration system. Russia's population now stands at about 14.7 crores. Putin's party United Russia holds a large majority and the parliament is stocked with faux opposition parties that actually support Putin. "As you know, the president is the head of the Security Council", he said.
Among other things, Putin proposed approving priority of the Constitution over worldwide treaties.
Mishustin vowed to focus on social issues and improve living standards.
He added that new weapons systems would protect Russia's security "for decades ahead".