Dvorkovich replaced Igor Shuvalov, who was recently appointed a first deputy prime minister in Russia's new Cabinet.
Dvorkovich, 36, was also earlier appointed by the president to the post of one of the seven presidential aides.
He was formerly a senior economic adviser to President Vladimir Putin, who became prime minister on May 8, a day after Medvedev had been sworn in as president.
In a series of new administrative appointments on Monday, President Medvedev also reappointed four officials as heads of presidential administration departments.
The president reappointed Oleg Govorun to the post of head of the presidential administration department on domestic policy; Vladimir Osipov - on personnel issues and state awards; Sergei Dubik - on state service issues; and Dmitry Zhuikov - on issues concerning citizens' constitutional rights.