Putin telephoned Naina Yeltsina, Yeltsin's widow, to express his condolences, a Kremlin spokesman said.
Putin said it was thanks to Yeltsin that "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.
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.
Bill Clinton, the former US president who together with Yeltsin brought about the warmest post Cold War Russia-US relations, called him courageous and steadfast.
"He risked his life to prevent a coup, then pushed Russia forward through economic hardship and political turmoil to partnerships with Cold War adversaries and membership in the G8.
"Fate gave him a tough time in which to govern, but history will be kind to him because he was courageous and steadfast on the big issues - peace, freedom, and progress," Clinton said.
Mikhail Gorbachev, the last president of the Soviet Union and Yeltsin's predecessor, said Yeltsin had done "great deeds" but also made "serious mistakes".
"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 called him "an historic figure during a time of great change and challenge for Russia".
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 and precipitated 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, said Yeltsin "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".
But a Chechen separatist website said Yeltsin - who sent Russian troops to put down a rebellion in Chechnya - was a war criminal for crimes against humanity.
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.
Source: Al Jazeera and agencies