The deal is a major step in the liquidation of what was once the fourth-largest investment bank in the U.S.
It comes a day after Nomura's announcement it was buying Lehman's Asian businesses for $225 million. A British bank, Barclays, has acquired Lehman's North American investment banking operations.
Nomura did not give a price tag for the acquisition of Lehman's European and Middle Eastern operations.
Lehman's parent company, Lehman Brothers Holdings Inc., sought bankruptcy protection eight days ago in the biggest Chapter 11 filing in U.S. history.
"This transaction will significantly extend our European footprint and international reach, enabling us to realize our strategy of delivering Asia to the world," Kenichi Watanabe, Nomura's CEO, said in a statement.
The Japanese brokerage company said it would take over Lehman's equities and investment banking operations in Europe and the Middle East.
There are around 2,500 staff for Lehman's European and Middle Eastern operations. Nomura said "a significant proportion" of them would be retained after the takeover.