Putin has said he will work closely with the new president.
He will set up a new cabinet, which is expected to be broadly similar to one that was in place during his eight-year presidency.
He selected Medvedev as United Russia's candidate for a presidential election in March, which Medvedev won by a wide margin.
|Medvedev was hand-picked by Putin to |
become Russia's president [AFP]
Jonah Hull, Al Jazeera's correspondent in Moscow, said Putin would aim to boost the profile of the prime minister's office after its role was minimised during his presidential term.
"The potential is now there to create a system of two centres of power, with checks and balances between Putin and Medvedev - something that Russia, in its political system since the Soviet era, has not had," he said.
"[During his presidential term] Putin went out of his way to bolster his presidency and to create a top-down system of government in which the president was unchallenged and unchallengeable.
"There is going to be a certain amount of change in the power sharing arrangement - but there is not, if Putin is to be believed, going to be any change to the constitution."
Although Putin and Medvedev are political allies, some analysts have said that the partnership could be unstable.
After he won the presidency in March, Medvedev said only the president would determine foreign policy, but Putin has called the prime minister's office the "highest executive power in the country".
In his inaugural speech on Wednesday, Medvedev promised to bring greater "civil and economic freedom" to Russia.
He also said he would strive to ensure that the rule of law is upheld.
Shortly after he took the presidential office, Medvedev was presented with a briefcase containing controls for Russia's nuclear arsenal.
Both Medvedev and Putin will attend a military parade in Moscow's Red Square on Friday, where Russia's new Topol-M intercontinental ballistic missiles will be displayed.
The Victory Day parade is the biggest display of Russia's military might since the end of the Soviet era in 1991.