Past US presidents Bill Clinton and George Bush senior, who both served in the White House during Mr Yeltsin's tenure at the Kremlin, attended.
Thousands of mourners earlier filed past Mr Yeltsin's coffin in the Church of Christ the Saviour in Moscow, where his body was laid in state.
The funeral of the first democratically-elected president of Russia took place at around midday within the cathedral, which was restored by Mr Yeltsin after being destroyed during the Soviet era.
In a fitting move the former Russian leader, who oversaw the break-up of the Soviet Union, was subsequently buried in the city's Novodevichye cemetery, rather than in Red Square, where many prominent Communists are interred by the Kremlin wall.
Mr Yeltsin died of heart failure on Monday, at the age of 76.
In a tribute to the former Russian head of state, the country's existing president Vladimir Putin said earlier this week that Mr Yeltsin had been responsible for the adoption of a new constitution which had given Russia's people the opportunity to "freely express" themselves.
However critics argue that the democracy established by Mr Yeltsin in Russia has been curbed by Mr Putin, who has declared today as a national day of mourning in memory of his predecessor.
Mr Yeltsin, who was elected to succeed the Soviet Union's last leader Mikhail Gorbachev in 1991, has been described by British premier Tony Blair as a "remarkable man" who saw the need for democratic and economic reform in Russia.
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