Medvedev's brief announcement, almost certainly approved in advance by Putin, was the second major development from the Kremlin in as many days, following Putin's Monday endorsement of a Medvedev bid for the presidency.
In this way, Putin and his longtime aide appear to answer a question that has long been the subject of conjecture and anxiety: whether Putin would relinquish power, and if so to whom.
The emerging scenario - one that Putin himself hinted at months ago - would see the popular president wielding considerable and possibly ultimate power from a beefed-up prime minister's position. Putin, who took over from Boris Yeltsin about eight years ago, is prevented by the constitution from holding a third consecutive term.
In a three-minute televised speech, Medvedev said Putin "prevented the collapse of the economy and social sphere in our country, a course that prevented civil war."
It was vital, therefore, to retain Putin's team, he said. "Therefore I think that is principally important for our country that we keep in the most important post in government - the position of chairman of the Russian government - Vladimir Vladimirovich Putin," he said.
"Having expressed my readiness to run for president of Russia, I appeal to him with a request to give his principal agreement to head the Russian government after the election of the new president of our country," Medvedev said.
Putin clearly wants to retain a powerful role once he steps down. Medvedev's proposal would provide such a role, especially if the constitution were amended to increase the prime minister's powers - which could be done readily with the new parliament dominated by pro-Putin politicians.
Putin's support virtually ensures that Medvedev would win the presidency, and Putin's enormous influence with parliament, where his party controls 70 percent of the seats, ensures he could become prime minister if he chose.
At a Kremlin meeting Tuesday with Yevgeny Primakov, the influential Yeltsin-era prime minister who now heads the Russian Chamber of Commerce, Putin made no reference to his annoited successor or the possibility of becoming prime minister.
Medvedev's announcement suggested that he would essentially serve as a figurehead controlled by Putin.
The 42-year-old lawyer from St. Petersburg projects a milder and more sympathetic image than the steely and occasionally bitingly sarcastic Putin. Medvedev's comments Tuesday, though, echoed Putin's often-expressed prickly national pride and distrust of the West.
"The world's attitudes toward Russia have been changed," Medvedev said. "They don't lecture us like schoolchildren. They respect us and they reckon with us. Russia has been returned to its overpowering position in the world community."
Medvedev, who currently serves as a first deputy prime minister, also praised efforts under Putin to restore the country's armed forces after years of post-Soviet neglect and underfunding.
"Our military defense and security have been increased," he said.
Unlike some of his powerful colleagues in the Kremlin, Medvedev is not a veteran of the KGB or other Russian security services. He has never run for elected office, and has spent most of his working life as Putin's aide.
While the Kremlin has packaged Medvedev as a liberal, giving him responsibility for social programs, Medvedev's political views are unknown. He is best known as a technocrat proficient at finding creative ways to implement Putin's policies.
As president, Medvedev's duties would include directing the work of the chiefs of the Federal Security Service, and the Federal Drug Control Service. But both agencies are headed by powerful KGB veterans - Nikolai Patrushev and Viktor Cherkesov, respectively - with close ties to Putin.
With no power base of his own, Medvedev could have found it difficult to direct these figures. Putin will have no such problem.
Pentagon officials said that Russia has developed a very powerful weapon, which Western specialists have already dubbed as the "doomsday weapon"
The head of the Russian Finance Ministry, Anton Siluanov, said that the Americans would suffer additional losses if they impose sanctions on Russia's public debt