The widow of Mr Yeltsin was among those attending an earlier funeral service for Mr Rostropovich at Moscow's Church of Christ Saviour, where a ceremony to remember the former head of state was also held on Wednesday.
Celebrated musician Mr Rostropovich died on Friday at the age of 80 following a battle with intestinal cancer.
Serving Russian president Vladimir Putin was among thousands of mourners who yesterday filed past his open coffin at the Moscow Conservatory, where Mr Rostropovich once studied.
Mr Putin has described the cellist's death as a" huge loss" for Russian culture.
Meanwhile the wife of French president Jacques Chirac and Spain's Queen Sofia were among dignitaries attending today's funeral, Russian news agencies reported.
Mr Rostropovich, who played a Bach suite below the Berlin Wall as it was being pulled down in 1989, fled his homeland and went to live in the West in the mid-1970s, having sparked anger within the former Soviet regime as a result of his support for dissidents such as Nobel Prize winner and writer Alexander Solzhenitsyn.
The cellist, who subsequently had his Soviet citizenship revoked, was finally able to return to Russia to perform after it was restored in 1990 by then Soviet leader Mikhail Gorbachev.
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