The purchase of Greenwich from the Long Term Credit Bank of Japan follows NatWest's recent purchases of Gleacher, a mergers and acquisitions adviser, and Gartmore, the UK fund manager.
Martin Owen, chief executive of NatWest Markets, the bank's corporate and investment banking arm, said: "This acquisition completes the major strategic moves needed to build a strong competitive position in the US.
"We now have critical mass in the US government bond markets, providing strong institutional distribution and trading expertise. We will also have leading skills in asset-backed securities. This will be a strong platform on which to develop our position in the global bond markets," Mr Owen added.
NatWest Markets has 6,500 staff in 24 countries and provides risk management, foreign exchange, securities sales, trading and research to institutions.
Greenwich, which is in the top 10 among fixed income firms in the US, was bought by LTCB of Japan in 1988 for US$140m (pounds 85m) becoming the Japanese bank's primary US operations unit.
Its capital markets arm has an average daily clearing volume of more than $20bn and is a leading underwriter and dealer in US Treasury, mortgage and asset-backed securities. The company is also a broker in exchange- traded options.
In 1995, Greenwich, which employs 400, recorded pre-tax profits of US$75m, down slightly on its previous year's total of US$76.4m, achieved during the 1994 bear market in bonds.
Mr Owen said: "The Greenwich management team have proven expertise and a disciplined approach which has built a consistently profitable fixed- income business. This will be a very strong position to build our position in the global bond markets."
He added that NatWest's interest in Greenwich followed the bank's decision to acquire a strong presence in US government bond trading and related derivatives. Organic growth was considered but not chosen because it would not have led to a market-leading position in the time desired.
Greenwich had been identified some months ago as being potentially for sale by LTCB, which has suffered bad loans problems in Japan.
Discussions between NatWest and Greenwich began in earnest several weeks ago after the US firm was given the go-ahead by its Japanese parent.
Greenwich's joint chief executives and co-presidents, Gary Holloway and Konrad Kruger, will jointly head NatWest Market's global fixed- income arm.