Mr Medvedev describes himself as pragmatic and business-friendly
"I fully support this candidacy," Mr Putin was quoted as saying.
Mr Medvedev was nominated by Mr Putin's United Russia Party and three other pro-Kremlin parties on Monday.
Mr Medvedev was previously Mr Putin's chief of staff and is chairman of the gas giant Gazprom. He hails from Mr Putin's native St Petersburg.
The 42-year-old former lawyer managed Mr Putin's election campaign in 2000. As first deputy prime minister he has overseen national programmes in the areas of health, housing and education.
HAVE YOUR SAY He seems like a solid individual who will appeal to the next generation of Russians
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He has long been a significant player in Mr Putin's group of close associates from St Petersburg.
His name was put forward by United Russia, A Just Russia, the Agrarian Party and Civil Force, at a meeting with President Putin.
Commenting on the choice, Mr Putin said: "I have known him for more than 17 years, I have worked with him very closely all these years, and I fully and completely support this candidacy".
Likely winner
The BBC's James Rodgers in Moscow says the overwhelming support for Mr Putin in Russia puts Mr Medvedev in a strong position to win the presidential election next March.
He will be officially nominated by a special congress next week as the United Russia candidate.
Fellow First Deputy Prime Minister Sergei Ivanov had also been seen as a strong potential presidential candidate.
Under Russia's political system the president enjoys far-reaching powers, including the appointment of regional governors.
Earlier this month United Russia won the parliamentary election by a wide margin, and Putin supporters will dominate the new parliament.
Mr Putin has made it clear he will retain a significant national leadership role after he leaves office at the end of his second term.
Mr Putin voiced confidence that Mr Medvedev would provide continuity.
"We have the chance to form a stable government after the elections in March 2008. And not just a stable government, but one that will carry out the course that has brought results for all of the past eight years," Mr Putin said.
United Russia leader Boris Gryzlov highlighted Mr Medvedev's role in managing national projects aimed at raising Russian living standards.
"Dmitry Anatolyevich (Medvedev) oversees national projects. He oversees the demographic programme and we believe that it is precisely the issues to do with raising standards of living that are the most important issues for the upcoming four-year period."
Dmitry Medvedev on July 27, 2007. 
Today, Dmitry Medvedev was named the candidate for  of Russia by the ruling party , which holds majority in the newly-elected State Duma, the lower parliament of Russia. 

Medvedev, who is the current deputy prime minister of the  and the chairman in the board of directors of , was also backed by three other parties and by the current president Vladimir Putin. This means the highly anticipated decision about the supposed successor has been announced.

"I have known him for more than 17 years, I have worked with him very closely all these years, and I fully and completely support this candidacy," Putin said. "We have the chance to form a stable government after the elections in March 2008. And not just a stable government, but one that will carry out the course that has brought results for all of the past eight years."

The declaration was unofficial: the formal nomination is expected on December 17, during United Russia's party conference.

The  is scheduled to be held on March 2, 2008.