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Under the deal, Orix will buy a 90.1 percent stake in Robeco from Dutch lender Rabobank, which will keep the remaining 9.99 percent stake.
The deal would help Orix strengthen its presence in the global asset management business, giving it an opportunity to offer Robeco's financial products to Japanese customers, it said.
"The financial market has drastically changed since the financial crisis," Orix said in a statement. "Orix has been seeking to build its presence in the global asset management industry in recent years."
Rabobank chairman Piet Moerland said: "Rabobank and Robeco have strengthened each other over the past decades by working closely together in serving their clients.
"This cooperation will remain... Robeco now has the opportunity to develop further under Orix's ownership."
Orix operates mainly in Asia and the Middle East with the acquisition giving them a strong foothold in the European and US asset management business. It has previously made smaller acquisitions in the United States.
Tokyo-based Orix, which operates in more than two dozen countries and has nearly 19,000 employees, is involved in a wide range of businesses including leasing and loans, insurance, and real-estate financing.
Robeco, which has 1,500 employees, manages about 189 billion in assets.
Japanese firms have been on a global buying spree in recent years as the strong yen and shrinking domestic market pushes them to look abroad to grow their businesses.