"I promised you we would win, and we won," he said, his eyes watering. "Glory to Russia!"
"We have won in an open and honest battle.
"We proved that no one can force anything on us."
Slogans on the banner included "Putin - our president" and "We believe in Putin".
Mr Putin, who supported Mr Medvedev in the Kremlin race in 2008 and became prime minister because of a constitutional ban on a third consecutive term as president, will now be in office until 2018. He could then run for another six-year term.
There was tight security around the capital, with 6,000 extra police brought in from outside.
'Grandiose scale of falsifications'
On Monday morning the electoral commission said that with more than 99% of the votes counted, Mr Putin won 63.75%, enough to give him a first-round victory over nearest rival Gennady Zyuganov, who polled 17.19%
The other three candidates were in single digits.
The turnout is predicted to be about 63%.
After the polls closed, Mr Zyuganov - the leader of the Communist Party who has previously been relatively loyal to Mr Putin - described the elections as "unfair and unworthy".
But he said that with increasing public anger, Mr Putin "would not be able to rule like he used to".
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