Blavatnik's all-cash deal for Warner values the world's third-largest music company at $8.25 a share plus debt.
The acquisition adds to Blavatnik's roster of media companies such as Russia's Amedia, Scandinavian mobile data and voice services provider ice.net and Britain's Top Up TV.
It also cements a long relationship between the Russian-born billionaire and Warner Music chief executive Edgar Bronfman Jr. and his father. Blavatnik bought Bronfman Jr.'s house in 2007 for $50 million, 11 times what the music chief had paid for it 12 years earlier.
Blavatnik is likely to keep Warner Music's management in place and turn to the team to lead a run for EMI. If that is successful, he could be rewarded with a quick return on his investment by combining the companies and saving hundreds of millions of dollars in costs.
EMI is owned by Citigroup, which took control of the company after its former private equity owner Terra Firma defaulted on loans.
Blavatnik agreed to pay a 63 percent premium to Warner's share price on Jan. 20 when news broke that the music company's board had assigned advisers to explore its strategic options — including a sale.
Warner Music will become an autonomous unit of Access. It will sit alongside industrial assets, including natural resources and chemicals, as well as media and telecommunications.
Blavatnik beat out last-round bids from Tom and Alec Gores' Platinum Equity/The Gores Group and Sony in partnership with Guggenheim Partners and investor Ron Perelman.
Bloomberg reported Friday that the Gores are weighing a counter offer to Blavatnik's bid of $8.35 to $8.50 for Warner, citing one source. A spokesman for the Gores declined to comment.
Blavatnik, 53, has been a U.S. citizen since 1984. He ranks No. 80 on the Forbes world billionaires list released in March, with a net worth of $10 billion.
Blavatnik became a director at Warner Music in 2004, when Bronfman led a private equity buyout of the company from Time Warner. Although he stepped down from the board in 2008, he retained a 2 percent stake in Warner Music.
Known for his investments in natural resources and chemicals, Blavatnik is also a director of aluminum giant United Company RusAl.
Bronfman and private equity firms Thomas H. Lee Partners and Bain Capital Partners together hold about 56 percent of the company's outstanding shares and have entered into a voting agreement with Access to vote in favor of the merger.
Thomas H. Lee Partners will make a return of about two times its original $655 million investment on sale of Warner Music Group to Access Industries, a source familiar with the investment said Friday.
Taking Warner Music away from the demands of being publicly traded is seen as an opportunity for Warner Music executives to take a bigger gamble on refocusing the company's traditional business model in the face of shrinking sales, rampant piracy and an uncertain digital future.