Vladimir Putin, the current president, telephoned Naina Yeltsina, the former president's widow, to express his deepest condolences, a Kremlin spokesman said.
"A man passed away, thanks to whom a whole new epoch was born. New democratic Russia was born, a free state open to the world. The state in which power truly belongs to the people," Putin said in a statement.
He also declared Wednesday a day of mourning for his predecessor.
Yeltsin was fundamental in dismantling Russia's communist rule and replacing its socialist economy with free-market capitalism - a programme that devastated the living standards of much of the population.
Mikhail Gorbachev, the last president of the Soviet Union, expressed his condolences on Monday.
"I offer my deepest condolences to the family of a man on whose shoulders rested many great deeds for the good of the country and serious mistakes - a tragic fate," he was quoted by Interfax as saying.
The White House offered its condolences to his family and his country.
"He was an historic figure during a time of great change and challenge for Russia. Our condolences go to Mrs Yeltsin, their family and the people of Russia," Gordon Johndroe, a US national security spokesman, said.
Yeltsin will perhaps be best remembered for climbing onto a tank sent into Moscow in 1991 by communist leaders attempting a coup during the final days of the Soviet Union.
His defiance galvanised crowds of pro-democracy supporters ahead of the collapse of the USSR in December 1991.
This made him a hero to many in the West but many Russians are still unable to forgive Yeltsin for Russia's slide from superpower status to economic crisis.
Sympathy and grief
"Boris Yeltsin has been well-and-truly off the political and public stage in Russia for seven years, since his resignation speech and the ascendancy of President Putin," Jonah Hull, Al Jazeera's Moscow correspondent, said.
"People have been very keen to forget the memory of the 1990s ... they haven't paid a lot of thought or attention to what had become of Boris Yeltsin and as a result I don't think there will be waves of sympathy and grief through the Russian public."
Tony Blair, the British prime minister, spoke of his sadness on hearing of the former president's death..
"He was a remarkable man who saw the need for democracy and economic reform and in defending that reform he played a vital role at a crucial time in Russia's history," he said in a statement.
Viktor Chernomyrdin, who served as prime minister under Yeltsin, spoke of the tol of the presidency on his health.
"Boris Yeltsin ruled the country at the most difficult time and this could not but impact on the health of such a naturally strong and healthy man," he said.
Yeltsin was born to a peasant family in 1931 near the city of Yekaterinburg in the Ural mountains and became a construction engineer before embarking on a political career in the Communist Party.