White-robed Russian Orthodox priests presided over Wednesday's ceremony which, according to custom, took place three days after Mr. Yeltsin died of a heart attack. He was 76.
The services were held inside the golden-domed Christ the Savior Cathedral, which was rebuilt during Yeltsin's time in office, after having been blown up by Soviet leader Josef Stalin.
One priest officiating at the ceremony said the Russian people had a strong desire to live in freedom and that Mr. Yeltsin helped to make that desire a reality.
He added that Mr. Yeltsin, a man of strong character as he put it, took responsibility for the country in a time of difficult, radical change.
Yeltsin's wife, Naina, and their two daughters sat close to the open, flag-draped coffin and were crying.
Russian President Vladimir Putin postponed his annual state-of-the-nation address until Thursday, in order to attend the funeral, along with hundreds of other dignitaries.
Former Soviet President Mikhail Gorbachev, Former British Prime Minister John Major, Polish Solidarity leader Lech Walesa, and former US Presidents Bill Clinton and George H.W. Bush attended the memorial service.
Mr. Yeltsin is remembered for challenging the Soviet establishment and being the driving force behind an agreement to split up the Soviet Union into independent states. But his years in office were also marred by economic collapse, political chaos and a costly, humiliating war against Chechen separatists.
After the ceremonies, the funeral cortege made its way to the 16th century convent, alongside the Moscow River. Red carnations, the traditional mourning flower in Russia, were strewn along the road leading to the burial site.
Mr. Yeltsin is the only Kremlin leader since Nikita Khrushchev -- ousted in 1964 -- not interred by the Kremlin Wall on Red Square. At the family's request, Yeltsin was laid to rest next to major Russian authors, musicians and artists, rather than alongside political or military leaders.
Over the past two days, thousands of ordinary Russians paid their respects as his body lay in state.