An anti-Kremlin rally late on Tuesday was stopped by a series of police raids before it began, with security forces on the streets of the capital to prevent any dissent.
Rise to power
Medvedev's inauguration caps a rise from being a Putin-era bureaucrat to the leader of the world's largest energy producing country.
He campaigned in March's presidential election on a promise to follow a plan engineered by Putin.
Medvedev's first important act will be to formally name Putin as Russia's prime minister, after which they will both attend a military parade at Red Square on Friday.
Two thirds of Russians believe that Putin will control Medvedev despite being in a less prestigious office, according to a poll released in April by the Levada Centre, a public opinion survey organisation.