The Kremlin restored his citizenship in 1990 in the new spirit of openness under Soviet leader Mikhail Gorbachev.
Within days of the Berlin Wall coming down in 1989, Rostropovich took his cello to Berlin to play at an impromptu concert by the remains of the wall.
"It was a call of the heart," he said later.
Among about 1,000 mourners were his widow, soprano Vishnyevskaya, Yeltsin's wife, the Queen of Spain and the wife of Jacques Chirac, the French president.
A plain wooden Orthodox cross was erected at the grave and lush wreaths placed around it before mourners applauded the musician for the last time. Some kissed his picture at the foot of the grave.
"He was ... a guiding light both as a citizen and as a musician," said pensioner Yelena Zubkovskaya who came to Rostropovich's funeral service at Moscow's Christ the Saviour Cathedral earlier on Sunday. "We will miss him."
Zubkovskaya added that she had attended every concert by Rostropovich she could, including the last one before his departure from the Soviet Union in 1974 which, she said, earned him a 10-minute standing ovation.
'The great cellist'
|"He was ... a guiding light both as a citizen and as a musician...we will miss him"|
Yelena Zubkovskaya, pensioner
Lyudmila Nuksunova, a music teacher in her 30s, said: "He was dear to me as a person, as a musician, as a family man."
She said she had skipped work to come to the cemetery: "I couldn't be anywhere else today."
More than 4,500 people came to Rostropovich's funeral service at the cathedral, RIA agency said.
Russian news agencies quoted a source close to the musician as saying
that Rostropovich had died in a Moscow hospital after a long illness.
His death was announced four days after that of Yeltsin, whom Rostropovich joined on the barricades to resist a coup by Soviet hardliners in 1991.
Rostropovich was one of Russia's best-loved cultural figures and considered among the world's greatest cellists.