Yeltsin oversaw a period of immense change in Russia
Mr Yeltsin - who had a history of heart trouble - died of heart failure in hospital at 1545 (1145 GMT).
He came to power after being promoted by former Soviet leader Mikhail Gorbachev, a man he then outmanoeuvred.
He won international acclaim as a defender of democracy when in August 1991 he mounted a tank in Moscow.
In what became one of the defining moments of his career, Mr Yeltsin rallied the people against an attempt to overthrow Mr Gorbachev's era of glasnost and perestroika.
In another episode of high drama, two years later he ordered Russian tanks to fire on their own parliament in October 1993, when the building was occupied by hardline political opponents.
YELTSIN KEY DATES July 1990: Resigns from Communist Party June 1991: Elected president of Russian republic (in USSR) August 1991: Rallies citizens against anti-Gorbachev coup, bans Russian communist party December 1991: Takes over from Mikhail Gorbachev as head of state 1992: Lifts price controls, launches privatisation October 1993: Russia on brink of civil war, Yeltsin orders tanks to fire at parliament December 1994: Sends tanks into Chechnya June 1996: Re-elected as Russian president, suffers heart attack during campaign 1998: Financial crisis, rouble loses 75% of its value December 1999: Resigns, appoints Vladimir Putin successor
Obituary of Yeltsin In quotes: Reaction to death
But Mr Yeltsin, who became Russia's first democratically-elected leader after Mr Gorbachev resigned in December 1991, saw his final years in office overshadowed by increasingly erratic behaviour and plummeting popularity as the economy suffered.
Bouts of ill-health were accompanied by rumours of a drinking problem, exhibited most famously when Mr Yeltsin grabbed a conductor's baton in Berlin and, apparently inebriated, tried to sing along with the orchestra.
The BBC's diplomatic correspondent Bridget Kendall says despite his unpredictability, Boris Yeltsin remained a reliable Western ally, even when relations grew icy over Nato's military action against Yugoslavia in 1999.
He announced his retirement in the final hours of 1999, handing over to former secret service chief Vladimir Putin, who was prime minister at the time.
Mr Yeltsin may have disappointed Russians by bringing them neither peace nor prosperity, our correspondent says.
But, she adds, he did help end 70 years of Soviet Communism, and that, in the long run, is what he will probably be remembered for.
Mr Gorbachev paid a mixed tribute to his successor, saying Mr Yeltsin was responsible for "many great deeds for the good of the country and serious mistakes", Russia's Interfax news agency reported.
Mr Putin has telephoned Mr Yeltsin's widow, Naina, to express his condolences.
The US White House praised Mr Yeltsin as an "historic figure during a time of great change and challenge for Russia".
A funeral for the former Russian president will take place at Moscow's Novodevichy cemetery on Wednesday 25 April.
President Putin has also declared that a day of national mourning.
"We will do everything we can to ensure that the memory of Boris Nikolayevich Yeltsin, his noble thoughts and his words ''take care of Russia' serve as a moral and political benchmark for us," he said in a televised address.
Chechen debacle
Mr Yeltsin's eight years in power brought immense changes to Russia.
I cannot shift the blame for Chechnya... I made the decision, therefore I am responsible
Boris Yeltsin
The BBC's Russian affairs analyst, Steven Eke, says under the Yeltsin leadership, Russians were given greater political and civic freedoms than they had ever enjoyed.
The media, especially television, were able to criticise the authorities, even the president, in a way they would no longer consider possible, he says.
But history may judge Mr Yeltsin's actions towards the rebellious region of Chechnya much more harshly, he adds.
In 1994, Mr Yeltsin launched a disastrous large-scale military intervention in the breakaway republic, pledging to crush resistance in days.
Instead, a bloody war of attrition ensued, which left tens of thousands of people dead, and the north Caucasus permanently destabilised
Speaking in an interview with Russian television in 2000, Mr Yeltsin said that he saw the lives lost in Chechnya as the biggest responsibility he had to bear.
But he added that there had been no alternative and that Russia had to act against Chechen separatists.
"I cannot shift the blame for Chechnya, for the sorrow of numerous mothers and fathers," he said. "I made the decision, therefore I am responsible."
Boris Yeltsin in 1993
Former President of Russia Boris Yeltsin has died at age 76, according to a Kremlin spokesperson.

"Today, at 15:45 (11:45 GMT) Boris Nikolayevich Yeltsin died in the Central Clinical Hospital as a result of a deteriorating cardio-vascular problem," said the spokesperson. Yeltsin had a history of heart problems.

Boris Nikolayevich Yeltsin (Russian: Бори́с Никола́евич Е́льцин) was the first President of the Russian Federation from 1991 to 1999. The Yeltsin era was a traumatic period in Russian history— marked by widespread corruption, economic collapse, and enormous political and social problems.

Yeltsin maintained a low profile since his resignation, making almost no public statements or appearances. However, on February 1, 2006, Yeltsin celebrated his 75th birthday. He used this occasion as an opportunity to criticize a "monopolistic" United States foreign policy, and to state that Vladimir Putin was the right choice for Russia.