Analysts said the apparently perverse reaction was because the tone of Mr Greenspan's comments, in his twice-yearly Humphrey Hawkins testimony to Congress, suggested market expectations of an immediate rise in rates were too pessimistic.
In early afternoon trading, the dollar fell but the Dow -Jones index was up around 70 points to 5,444 and US bonds and British gilts were buoyant.
In London, shares closed 35.2 higher at 3,693.4 on the FT-SE 100 index.
The prospect of a rising trend in interest rates was one of the reasons behind the sharp sell-off in US markets earlier this week. Analysts added that investors might have gone short ahead of the meeting, and the rally reflected unwinding of their positions.
Mr Greenspan's indication that the US interest rate cycle might be turning, with the first rate rise since February 1995, came a day after it emerged that Eddie George, Governor of the Bank of England, opposed last month's cut in sterling interest rates and that he also expects the UK interest rate cycle to turn up in the not too distant future.
In his warning of a possible rate rise, Mr Greenspan said that for some time Federal Reserve policy had been "designed to act pre-emptively" and he was "confident that the Federal Open Market Committee would move to tighten reserve market conditions should the weight of incoming evidence persuasively suggest an oncoming intensification of inflation pressures that would jeopardise the durability of the economic expansion".
The testimony included a carefully balanced assessment of the risks of a re-emergence of inflation which said that it was bound to happen, but gave no clear indication of timing.
Mr Greenspan said: "Clearly, in this environment, the Federal Reserve has had to become especially vigilant to incipient inflation pressures that could ultimately threaten the health of the expansion."Reuse content