US stock markets rallied in response, with the Dow Jones closing Tuesday's session down by just over 1 per cent after opening lower by almost 5 per cent.
Still, Wall Street registered its fifth day of losses and included a brief dip by the Nasdaq into bear market territory.
The Dow Jones industrial average was down 128.11 points, or 1.06 per cent, at 11,971.19, closing below 12,000 for the first time since November 3, 2006.
Japan's optimism appeared stronger, with the benchmark Nikkei index gaining 423.82 points, or 3.37 per cent, to 12,996.87 points on the Tokyo Stock Exchange in early Wednesday trade.
Hong Kong's Hang Seng bounced 7.4 per cent or 1,601.57 points to open at 23,359.20, a day after Hong Kong shares suffered their biggest ever one-day fall by closing down 8.7 per cent.
In China, share prices opened 2.69 per cent higher, rebounding from a steep decline in the previous two sessions.
The Shanghai Composite Index rose 122.61 points to 4,682.36, after closing down 7.22 per cent on Tuesday to mark the biggest daily drop since June 4, 2007.
Meanwhile Australian shares were also on a rebound, rising 5 per cent to recoup 12 days of losses.
The benchmark S&P/ASX 200 index was up 266.3 points or 5.1 per cent at 5,453.1, but dipped off an earlier peak of 5,540.7.
In South Korea, the Kospi rose 48.34 points, or 3 per cent, to 1,657.36 in the opening minutes of trading. It had dropped 4.4 per cent on Tuesday.
European stock markets, which had dropped sharply on Monday and earlier on Tuesday, also rose following the interest rate cut.
The UK's FTSE 100 closed up 161.9 points at 5,740.1, having fallen as much as 4.3 per cent earlier in the day.
Latin American stocks also surged, with the Brazilian Bovespa rising 4.45 per cent after slumping 6.6 per cent in the previous session.
Trading of Mexican stocks was temporarily halted due to the high trading volume.
Al Jazeera's John Terrett said in New York that the Federal Reserve's move was to send a message that the leadership of the US economy was prepared to pull out all the stops to prevent a recession.
It was the largest single shift in interest rates since November 1994, when the bank raised rates by three-quarters of a point.
It was also the first rate cut in between regularly scheduled policy meetings since September 17, 2001, the first day US financial markets reopened after the September 11 attacks.
George Bush, the US president, said he hoped the $145bn economic stimulus plan he announced last week could be implemented quickly.
"Everybody wants to get something done quickly, but we want to
make sure it is done right, and make sure that everybody's realistic
about a timetable."
On Monday, European markets appeared to have decided that the package was insufficient to prevent a looming recession in America.
Markets there fell, while US markets remained closed for Martin Luther King Day.
The markets been volatile since last year when hundreds of thousands of low income US homeowners defaulted on loans which had been given out with little or no down payment.
The sub-prime crisis led to US lenders such as Citibank and Merrill Lynch announcing in recent weeks that they had lost tens of billions of dollars.
That situation in the US has been compounded by higher unemployment rates, rising food prices and oil prices at around $100 a barrel.