Sotheby's auctioneer earlier cancelled the auction for the collection of Russian art, set for September 18-19 in London, saying it had been "acquired privately in its entirety" and that the new owner intended to bring it to Russia.
The works, collected by Rostropovich and soprano Galina Vishnevskaya, are believed to be worth tens of millions of dollars. A source close to the auction house earlier reported that Usmanov was the buyer.
A spokesman for the businessman said: "We confirm that Alisher Usmanov has bought the collection. Details of the purchase will be made public later."
The auction house and the spokesman did not disclose the sum paid, but Sotheby's said it was "substantially higher than the highest presale expectations."
Uzbek-born Usmanov, who co-owns major steel factories, heads a subsidiary of state-controlled energy giant Gazprom and has invested in media, telecoms and banking, is Russia's 23rd richest man according to Forbes magazine, with estimated wealth of $5.5 billion.
In early September, he bought the rights to a collection of Soviet-era cartoons from U.S.-based film company Films By Jove (FBJ) and presented them to Bibigon, a new Russian children's channel proposed by President Vladimir Putin, which started broadcasting on September 1.
Mstislav Rostropovich died in April aged 80. The Rostropovich-Vishnevskaya collection, which includes paintings, porcelain and glassware, adorned the couple's properties in Paris and London after they were forced to leave the Soviet Union in 1974.
