The Izvestia newspaper said Medvedev had left government headquarters for a Kremlin office close to the outgoing president's.
Medvedev, a 42-year-old St. Petersburg lawyer, won a landslide victory in Russia's March 2 presidential elections after being publicly backed by Vladimir Putin.
Putin, who is to take up the post of prime minister, will soon move into the White House government building, where prime ministerial premises have been under reconstruction for over a month.
The prime minister's offices are being rebuilt to accommodate the energetic and businesslike Putin, 55, and his sprawling staff, the paper said, adding that hundreds of Putin's future aides had begun to move into the White House there several months ago.
The offices are being modernized to keep up with Putin's expected merciless demands of the press office and the protocol and liaison service, the newspaper said.
Political analysts have questioned exactly who in the Putin-Medvedev tandem will be in charge in the country. The popular Putin, barred by law from running for a third consecutive term as president in the recent elections, is expected by many to be the power behind the Kremlin throne.
Other experts have suggested that the position of premier could simply be temporary post before Putin seeks a third term in 2012.