The deal promotes Goldmans into the ranks of the world's top 25 money managers, with $85bn under management.
Fund management companies have been at a premium, particularly in London, since investment banks realised that fund management was vital in smoothing volatile earnings from their traditional securities and corporate finance activities.
Goldman refused to say how much it had paid for CINMan.
British Coal's attempts to wind down its activities since the sale of its mining business in 1994 have been hit by crises at CINMan. First there was a well-publicised row between British Coal and the pension fund's trustees, which was followed by the withdrawal of front-runner Friends Provident.
It had offered pounds 70m but failed to agree terms. Subsequent efforts to re-open negotiations with Dutch insurance group Robeco, second in the queue, were short-lived.
For Goldman the acquisition is an attempt to catch up with its "bulge bracket" rivals, Morgan Stanley and Merrill Lynch.
Peter Sutherland, chairman and managing director of Goldman Sachs International, said: "We look forward to a long and successful relationship with the two Coal pension schemes."
Analysts said Goldman had until now concentrated on the low-margin business of short-term money market funds.Reuse content