Putin has agreed to be his prime minister, the second highest post in Russia.
"Such a victory carries a lot of obligations," Putin said from the open-air concert stage outside the Kremlin. "This victory will serve as a guarantee that the course we have chosen, the successful course we have been following over the past eight years, will be continued."
Some voters complained of pressure to cast ballots for Medvedev, and critics called the election a cynical stage show to ensure unbroken rule by Putin and his allies.
Sunday's vote came after a tightly controlled campaign and months of political maneuvering by Putin, who appeared determined to keep a strong hand on Russia's reins while maintaining while maintaining the basic trappings of electoral democracy and leaving the constitution intact.
Some in the West have welcomed Medvedev's reputation as a moderate after years of tense ties with Putin over his crackdown on domestic dissent, U.S. plans for a missile defense and Kosovo's independence, among other things.
Few international observers monitored the election, in which accounts of pressure will reinforce Western concerns of backtracking on democracy under Putin.
"The result doesn't matter as this is an illegitimate transfer of power," said former Prime Minister Mikhail Kasyanov, a Putin foe who was barred from the ballot.
Kremlin spokesman Dmitry Peskov said; "These are free and democratic elections after a free and democratic campaign."
Some 450,000 police and troops deployed nationwide to ensure the voting proceeded calmly, although two bomb explosions targeted a police convoy near Chechnya, wounding several people.
Though he has never held elected office, Medvedev has had an easy ride toward the presidency. Polls predicted he would take a solid majority of votes against the three other candidates: Communist Gennady Zyuganov, flamboyant ultranationalist Vladimir Zhirinovsky and the little-known Andrei Bogdanov of the Democratic Party.
Liberal opposition leaders Kasyanov and Garry Kasparov, the former world chess champion and one of the Kremlin's most prominent critics, were both squeezed off the ballot on technicalities.
The ITAR-Tass and Interfax news agencies quoted Zyuganov saying he has a list of 200 alleged vote violations and Zhirinovsky as saying he will challenge official vote results in court.
Escorted by a dozen riot police as he spoke to journalists near Red Square, Kasparov carried a plastic shopping bag that read, "I am not participating in this farce."
Zyuganov claimed widespread irregularities but provided no evidence.
Only 300 international election observers were monitoring the 96,000 voting stations across Russia's 11 time zones. The influential Organization for Security and Cooperation in Europe refused to send observers, saying Russia imposed such tight restrictions that its mission would be meaningless.
With Medvedev hoping for a powerful mandate, turnout was the only electoral uncertainty. It stood above 60 percent nationwide two hours before the last polls were to close, the Central Election Commission said.
"All of my friends voted for Medvedev, they say he's been elected already and want to be part of majority." said Renata Mukhammetshina, 21, a student in the southern city of Volgograd.
Polling stations offered enticements to voters: discounted food, office supplies, concerts and flowers. That echoed Soviet times, when hard-to-get items were available during carefully staged elections. In a post-Soviet touch apparently aimed to boost turnout, some polling stations were set up in shopping malls.
Moscow street cleaners swept away grime for voting day. In the southern Russian city of Stavropol, public transport was free for the day. In Krasnodar, a local group staged a lottery open only to voters - with a car as the top prize.
In Medvedev's native St. Petersburg, some voters quaffed bargain beer at their polling place. Others showed up for the goods but didn't bother to vote.
Government-paid teachers and doctors across the country complained that they were being pressured to vote at their workplace under the gaze of their superiors to ensure a convincing win and a high turnout for Medvedev.
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 voters and voters being "bought off."
"Most of problems appear to be occurring at the local level" in the provinces, where there is little scrutiny, Liliya Shabanova said.
Observers from the Parliamentary Assembly of the Council of Europe complained to the election commission about disproportionate campaign airtime given to Medvedev.
Some cast protest ballots, including Alexander Petrov, a 28-year-old trader in the Pacific port city of Vladivostok who voted for Zyuganov because he wanted to "take away votes from the candidate of the ruling powers."
Sofia, 25, a history teacher in a school in southwestern Moscow, said the principal required her and her colleagues to cast ballots at a polling station at the school.
"This is terrible; they are not leaving us any choice," said Sofia, who declined to give her last name out of fear of losing her job. She said she destroyed her ballot in protest.
The new president's major domestic tasks are economic. Russia got rich from skyrocketing world oil prices, but the economy is hugely dependent on natural resources and needs to diversify to ensure long-term prosperity. Inflation - more than 11 percent last year - is undermining the nascent middle class.
Timofei Ryumin, 38, a doctor who lives in Russia's westernmost region, the Baltic city of Kaliningrad, said Medvedev's campaign seems "planned and coherent" and voted for him despite disappointment in the Kremlin's unfulfilled promises to provide cheaper housing for families like his.
"I don't see alternative leaders who could hold a firm grip on power," he said.
