Nearly final results -- from 99.45 percent of precincts -- showed that the 42-year-old Medvedev had received 70.2 percent of the vote, the head of the elections commission said Monday.
Shortly after almost all the votes were counted, hundreds of young people marched through Moscow toward the U.S. embassy to criticize American policies in Kosovo, Iraq and the Muslim world.
While they toed the Kremlin line, Gazprom, the Russian gas monopoly, made good on a promise to reduce gas supplies to Ukraine. In addition to serving as first deputy prime minister, Medvedev is chairman of Gazprom.
Russia says the dispute over natural gas with Ukraine is strictly a financial one, a result of the alleged nonpayment by Ukraine for past gas deliveries. But the timing of the cutoff suggests a possible deeper motive: telling the world that despite his purported liberal leanings, Medvedev plans to rule with a firm hand -- one perhaps guided by Putin himself.
The last time Russia cut gas supplies to Ukraine was in January 2006 in a move widely seen as punishment for the Orange Revolution that blocked a Kremlin-backed candidate from gaining Ukraine's presidency. Since then, Russia has expressed continuing anger over Ukraine's attempts to join NATO and forge stronger links with the European Union.
Chris Weafer, chief strategist for UralSib investment bank, said Medvedev may have been motivated by the need to appear tough in the face of Russia's dispute with Ukraine over gas payments.
"He found himself in that situation," Weafer said. "He didn't want to be seen as backing down."
Meanwhile, election observers from the Parliamentary Assembly of the Council of Europe, said Monday that unequal access to the media called into question the fairness of the vote.
Andreas Gross, who led the 22-member mission, described Sunday's vote as a "reflection of the will of the electorate whose democratic potential unfortunately has not been tapped."
Two of Medvedev's three challengers alleged there were violations and threatened to challenge the results in court.
The influential Organization for Security and Cooperation in Europe refused to send observers, saying restrictions imposed by Russian authorities monitors made it impossible to work in a meaningful way.
The campaign was dominated by Medvedev, the Kremlin's favorite, who refused to debate his rivals or formally campaign but received the bulk of the television coverage. In the end, no one was surprised by the result.
The liberal opposition alliance headed by former chess champion Garry Kasparov planned marches in cities around the country Monday. Riot police have used violence to break up similar marches in the past, and trucks of police were stationed early Monday near the square where the Moscow march was to begin.
The main outstanding question was who would be calling the shots in Russia once Medvedev takes over and, as is widely expected, names Putin prime minister. The outside world will watch closely how the new leadership in Russia, with its immense oil and gas reserves, engages with global rivals and partners at a time of rising commodities prices.
Most Russians expect the mild-mannered Medvedev to follow Putin's lead, at least at first.
In his rhetoric, Medvedev has presented himself as a pro-business liberal and more Western-leaning face to the rest of the world. But he has also helped implement Putin's drive to give the Kremlin a near-monopoly on political power and energy resources.
The teacher-pupil relationship will be tested after Medvedev's inauguration May 7. Medvedev has said he would propose making Putin his prime minister, and Putin has said he will accept the offer. But in Russia, the premier wields significantly less power than the president, and Putin may find his new chair confining.
Gazprom's reduction of gas to Ukraine could be an early signal of Medvedev's foreign policy. Another early sign could come in July at the summit of the Group of Eight leading industrialized nations: If Putin goes alone or accompanies Medvedev, that could signal his reluctance to relinquish control.
Some officials who know the quiet, unassuming Medvedev have said privately that he is tougher than his appearance and demeanor may suggest. Russian history also shows that rulers often like to get rid of those who backed their ascent to power.
Medvedev's election was not a wide-open contest. Medvedev ran against three rivals apparently permitted on the ballot because of their loyalty to the Kremlin line. But Communist Party candidate Gennady Zyuganov and ultranationalist candidate Vladimir Zhirinovsky still alleged violations after the voting ended.
Zyuganov, Medvedev's nearest challenger with almost 18 percent in the nearly complete results, said he would dispute the result. Zhirinovsky, with 9 percent, threatened to do so as well.
Liberal opposition leaders Kasparov and Mikhail Kasyanov were barred from running after authorities decided they had not met the strict requirements for gaining a spot on the ballot. Voters across Russia say they were being urged, cajoled and pressured to vote in an effort to ensure that Medvedev scored a major victory.