It was held in the Kremlin's magnificent St Andrew's Hall.
The ceremony began with an honour guard bringing in the symbols of the presidential office.
Mr Putin then made a short speech, describing the handover of power as "a hugely important stage" for Russia.
"It's extremely important... to continue the course that has already been taken and has justified itself," said Mr Putin, referring to his eight years in power.
Mr Medvedev then took an oath on a red-bound copy of the Russian constitution.
In a brief speech, he pledged to work for "a better" Russia, developing "civil and economic freedom".
He said that "human rights and freedoms... determine the meaning and content of all state activity".
Mr Medvedev also stressed he would "pay special attention to the fundamental role of the law".
He then thanked Mr Putin for his personal support, saying he hoped he would enjoy such backing in the future.
A 30-gun salute was then fired from the Kremlin embankment to mark Mr Medvedev's inauguration.
The grand ceremony was the expression of a new confidence that oil- and gas-rich Russia now feels, correspondents say.
Having campaigned as Mr Putin's protege and tied himself to his mentor's policies as soon as his victory became known, analysts say it is no surprise that Mr Putin will continue to play a central role.
Mr Putin urged Russians to support his successor
An economic liberal, Mr Medvedev has served Mr Putin as first deputy prime minister, chairman of Gazprom - Russia's enormous state-run gas monopoly, campaign chief and chief of staff.
But his working relationship with his predecessor goes back much further.
A lawyer by training, in the 1990s Mr Medvedev was an assistant professor at St Petersburg State University, during which time he became an expert consultant for the city administration - where one Vladimir Putin had a senior position.
And, analysts suggest, their partnership looks set to continue.
But the question of who wields the real power in the Kremlin will continue to fascinate, puzzle and perplex, the BBC's James Rodgers in Moscow says.
Mr Putin will remain Russia's most popular politician for the foreseeable future, which will give him huge influence over the man he mentored as his successor, our correspondent says.
'Wait and see'
The Kremlin's lack of tolerance for dissenters was highlighted on Tuesday as police detained dozens of would-be protestors in advance of a planned rally by The Other Russia, an opposition group led by world chess champion Garry Kasparov.
However, there are hopes - both in Russia and abroad - that the country will be changing under Mr Medvedev.
"Any day that you can exchange a member of the secret police for a law professor is a good day," international lawyer Robert Amsterdam, who represents jailed Yukos boss Mikhail Khodorkovsky, told the BBC.
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