Media giant Bertelsmann has agreed to buy the 25% in the business held by Belgium's richest man, Albert Frere, to avoid a public listing of the firm.
The German-based group is to pay 4.5bn euros ($5.8bn; £3bn) for the stake.
Mr Frere said at the start of the year that he wanted to see the shares float on the markets.
Family-run Bertelsmann indicated at the time that while it was prepared to see its shares float, it would rather keep the firm as a private company.
Bertelsmann - which owns Random House, the publisher of the Da Vinci Code, and 50% of music label Sony BMG - is buying the 25% stake from Mr Frere's investment vehicle Groupe Bruxelles Lambert.
'High price'
"This was the right move at the right time. The price is just right," said Bertelsmann's chief executive Gunter Thielen.
Bertelsmann wished to keep the business private to avoid the possibility of shareholders demanding short term moves which it did not consider to be in its long term interest.
The company is controlled by the Mohn family.
Analysts said the price Bertelsmann was prepared to pay for the 25% stake was "towards the high end of market expectations".
Bertelsmann is funding the purchase through a bridge loan provided by a number of banks.
Sony BMG's roster of artists range from Bruce Springsteen to Dido and Britney Spears.
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