Stocks in Japan have rebounded, with the Nikkei closing up 7.74%, breaking back through the 8,000-point barrier to end at 8,211.90, reported BBC.
In South Korea, the Kospi closed down slightly at 968.97 after shooting up more than 7% earlier in the day.
On Tuesday stocks on Wall Street ended with a 10% surge.
Analysts said investors were buying in anticipation that the Federal Reserve would cut interest rates on Wednesday, with a half-point cut to 1% predicted.
There are also hopes that interest rates will be cut by the Bank of Japan.
Meanwhile, companies which are highly dependant on export earnings - like camera maker Canon, saw their share price rise on the back of a weakening yen.
It was trading at 97.13 to the US dollar, falling back from a 13-year high last week.
On Tuesday, New York's Dow Jones index closed ahead 889.35 points, or 10.88% at 9065.12. The tech-based Nasdaq also closed up 9.53%, and the broader S&P 500 was ahead 10.79%.
That was the Dow's second biggest one-day points gain ever, after dropping 500 points on each of the two previous trading days.
Volatility has been the watchword over the past few weeks - out of 20 trading days there have been only two where the Dow did not close up or down by triple digits.
Shares of aircraft maker Boeing were up 15% to $48.91 after the manufacturer reached a provisional deal with its largest union to end a strike and end losses put at $100m (£64m) a day.
Earlier on Tuesday, in London, the FTSE closed up 73.79 points, or 1.9%, at 3,926.38 while in Paris the Cac 40 gained 47.57 points, or 1.6%, to end at 3,114.92.
Frankfurt's Dax rose 485.81 points, or 11.3%, to 4,823.45.
In Germany, the Dax was mainly boosted by Volkswagen, whose shares have soared since Porsche announced on Sunday that it had upped its VW stake. This has caused investors to scramble for the remaining VW shares in the market.
As a result, VW - Europe's largest carmaker - was the clear winner on the German index, finishing the day up 81.7% at 945 euros.