The deal values Fortress at $6 billion, with Nomura paying $888 million for the stake.
Under the deal, expected to close in January, Nomura will take ownership of Class A shares and the proceeds will go to the Fortress principals.
New York-based Fortress, established in 1998, now has around $26 billion in assets under management, including $9.4 billion of hedge funds and $13.6 billion of private equity funds.
The deal follows Nomura's expansion plans in a bid to compete on a globally and reduce its reliance on Japanese stock trading. Last month the firm bought complete control of global agency-broker Instinet.
Last month Fortress announced it was aiming to raise $750 through an IPO selling ten per cent of its stock.