Tokyo saw the most dramatic rise in share prices, with the Nikkei index rising nearly a thousand points in a single session.
In London, share prices enjoyed their biggest one-day rise since the pound left the European exchange rate mechanism in September 1992.
Wall Street followed suit, with news of a far bigger than predicted rise in the number of jobs last month failing to dent severely the view that US interest rates have now passed their peak.
"Governments are prepared to loosen the monetary framework in order to support growth. That has to be good for shares everywhere," Corey Miller, equity strategist at Societe Generale Strauss Turnbull, said.
The dollar and the pound also strengthened slightly thanks to moderate intervention by the US in conjunction with the Japanese authorities. The New York Fed bought $300m-worth of dollars. The boost encouraged foreign investors to return to Wall Street.
The Nikkei index rose 956 points to close at 16,213, the highest for nearly two months. Dealers in Tokyo welcomed the Bank of Japan's decision to ease the cost of credit in order to stimulate the depressed economy. A reduction in the official discount rate is expected to follow, and commercial banks are expected to reduce their prime rates next week.
However, some warned that the initial euphoria would fade. "The condition of the economy is very weak," Toshio Shibatani, president of NKU Investment Management, said. He predicted the Nikkei index could return to 15,000 next week. "The fundamentals still look extraordinarily grim," said John Shepperd, chief economist of Yamaichi International.
Many traders said the stock market still needs more action by the government.
In Britain, the FT-SE 100 index rose nearly 75 points to close at 3,462.9. Analysts said the gains were due to a combination of relief that the bout of political uncertainty had come to an end and anticipation that overseas interest rate cuts would reduce the need for a rise in base rates.
"The market has begun to recognise that the peak in base rates is not far," Mark Brown, chief strategist at Hoare Govett, said.
However, he warned that share prices now incorporated much of this good news, and added: "Political uncertainty could also come back to haunt us."
A surprisingly big rise in employment last month relieved fears that the US economy is poised on the brink of a recession. But yesterday's figures, which came a day after the Federal Reserve announced a small cut in a key interest rate, did not change the majority view that there will be further interest rate reductions this year. Brian Fabbri, the New York economist for Paribas, said: "The Fed is through with tightening policy for this business cycle. It has embarked on a course of reducing rates." The Dow Jones index was 29 points higher at 4693 by mid-afternoon.
The number of jobs created in June rose by 215,000, almost twice as many as expected. The unemployment rate dropped to 5.6 per cent.
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