Medvedev made the surprise announcement on Russia's state TV while sitting next to Putin who thanked him for his work.
"In this context, it is obvious that, as the government, we must provide the president with a capability to make all decisions" needed to execute the proposed plan, he said.
"After those amendments are adopted-and it was said that this is likely to be done following discussion-there will be significant changes not only to a variety of constitution articles, but to the balance of power, namely to the executive, legislative, and judicial branches of power", the prime minister said.
Governance is seen by Putin to be hampered by the lack of a direct constitutional line between president and ministers, and this would be resolved by making the prime minister the key person in the policy sphere rather than the president. "In this case, the president will be obliged to appoint them, that is, he will not have the right to reject parliament-approved candidacies".
At the same time, Putin argued that Russian Federation would not remain stable if it were governed under a parliamentary system.
Speaking to BBC's Today programme, former Prime Minister Mikhail Kasyanov said the President could be eyeing on running "forever".
Opposition leader and Kremlin critic Alexei Navalny said he believed Putin's goal remained to be Russia's "sole leader for life", and he expected any vote on constitutional changes to be "fraudulent c**p".
Notably, the Russian Constitution doesn't allow anyone to serve as the country's president for more than two consecutive terms.
Medvedev, who is one of Putin's oldest allies and served as president from 2008 to 2012, had become a scapegoat and a liability, with approval ratings of between 30 and 38 percent.
The Kremlin may have fallen in on itself, but one thing's for certain: Vladimir Putin is not going anywhere.
Putin emphasised that the constitutional changes must be put to a nationwide vote.
On Wednesday, he proposed expanding the State Council's role and enshrining its status in the constitution.
"There are rumors that Putin could lead the new State Council rather than becoming the new Prime Minister", Ignatov told CNN.
Russian President Vladimir Putin delivers his speech at a gala on the occasion of the New Year at the Bolshoi Theater in Moscow on December 26, 2019.
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.
Mishustin has been hailed for modernizing Russia's rigid tax administration system and boosting tax collection rates. Russia's population now stands at about 147 million.
In his state of the nation speech, Putin said he wanted more authority transferred to parliament from the president. He said that the president should have the power to name top defense and security officials.
Among other things, Putin proposed approving priority of the Constitution over global treaties.
Mishustin vowed to focus on social issues and improve living standards.
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