The Central Election Commission said Communist party leader Gennady Zyuganov had received 18.41%, nationalist Vladimir Zhirinovsky - 10.26% and the leader of the tiny, pro-Western Democratic Party, Andrey Bogdanov - 1.33%.
Turnout was around 65%, according to Central Election Commission figures.
"I would like to thank everyone who voted for me, and also those who voted for other candidates," said Medvedev at an election concert earlier in Red Square. "Together we represent almost two-thirds of our country."
"Together we will move further forward, together we will achieve victory!" he announced to the crowd.
Russian First Deputy Premier Medvedev was publicly backed by Russian President Vladimir Putin as his successor in mid-December, and was later nominated by the ruling United Russia party as a presidential candidate.
"The elections for the president of the Russian Federation have taken place. Our candidate has a firm lead," said Vladimir Putin, appearing alongside Medvedev.
The inauguration of Russia's new president is set for May 7.
Gennady Zyuganov and Vladimir Zhirinovsky earlier announced they may contest the results of the poll in court, citing voting violations.
Many Western observers, including the OSCE's main election arm, chose to boycott the election over restrictions imposed by Russia. Moscow rejected claims that it had imposed restrictions on monitors, however.
Critics also pointed to pressure on voters to cast their ballots, especially employees of state-run organizations.
A CIS election monitoring mission said the elections had been held in full accordance with the law. The CIS is an alliance of a number of former Soviet republics.
Election monitors from the Parliamentary Assembly of the Council of Europe have yet to comment on the polls.
