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 head of the elections commission on Monday released nearly final results from 99.45 percent of precincts showing that the 42-year-old Medvedev had 70.2 percent of the vote.
CBS News correspondent Elizabeth Palmer reports the opposition never had a chance. During the past year, police broke up opposition rallies and well-known candidates were barred from the presidential race on technicalities.
Not everyone accepted the results, and two of Medvedev's challengers threatened to go to court over alleged violations. The few independent international observers who monitored the vote were to release their assessment Monday.
Former Prime Minister Mikhail Kasyanov, who was barred from running in the election, called the vote, "a KGB Secret Service Operation with the name democratic elections." Putin is a former high ranking officer from Russia's notorious Cold War spy agency.
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.
In Washington, a White House official acknowledged Medvedev's victory Monday morning.
A statement released by spokesman Gordon Johndroe said: "The United States looks forward to working with him. It's in our mutual interest for Russia and the United States to work together on areas of common interest such as non-proliferation, counterterrorism and combating transnational crime."
The main outstanding question was who would be calling Russia's shots 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.
Palmer says there are some important differences between Medvedev and his successor.
"Putin was a KGB agent who resented the crumbling of the Soviet Empire," Palmer says, "Medvedev actively worked for democratic reforms in the 1990's. Also, he's worked in private business with foreign business people. Some liberals in Russia hope that - once he consolidates his power base - he will introduce reforms to control corruption and restore things like freedom of the press."
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.
At a news conference early Monday, Medvedev was asked who would run foreign affairs - him or the prime minister. "Under the constitution, the president determines foreign policy," he said.
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.
As a key implementer of Putin's polices, Medvedev is seen as unlikely to alter Putin's assertive stance with the West, reduce state control over Russia's mineral riches or allow more real opposition movements to flourish.
"Our candidate, Dmitry Anatolyevich Medvedev, has taken a firm lead," Putin said late Sunday, appearing alongside his protege at a celebration at Red Square outside the Kremlin.
Medvedev - pronounced med-VEHD'-ev - thanked voters and vowed to pursue Putin's policies.
"We will increase stability, improve the quality of life and move forward on the path we have chosen," Medvedev said. "We will be able to preserve the course of President Putin."
That 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.
One early sign could be the July 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 Medvedev say privately that he is tougher than his appearance and demeanor may suggest and could show more resolve after his inauguration. Russian history also shows that rulers often like to get rid of those who backed their ascent to power.
Medvedev will be the first Russian leader to succeed his predecessor according to a constitutional timetable; Putin became acting president first after Russia's first president, Boris Yeltsin, stepped down early, and only later won election.
But Medvedev's election was not a wide-open contest.
Liberal opposition leaders Kasparov and Mikhail Kasyanov were barred from running on technicalities, and voters across Russia say they were being urged, cajoled and pressured to vote in an effort to ensure that Medvedev scored a major victory.
Kasparov held his own protest against the election Sunday near Red Square. Escorted by a dozen riot police, he carried a plastic shopping bag that read: "I am not participating in this farce."
The head of an independent Russian election monitoring group, Golos, said her organization was receiving a steady stream of complaints and reports of irregularities, including blatant attempts to influence and bribe voters.