The news lifted the euro, which spiked above $1.30 in New York, but Japanese authorities expressed concern that a flood of cheap dollars would further strengthen the yen, which hit a seven-month high against the greenback late Thursday.
Tokyo shares rose 1.54 percent by the break, Hong Kong surged 2.40 percent, Sydney climbed 1.02 percent, Shanghai added 0.35 percent and Seoul advanced 2.42 percent.
After a two-day meeting, the policy committee of the central bank said it would start a third programme of purchasing $40 billion a month in mortgage-backed bonds, known as quantitative easing (QE3).
It said it would continue its monetary easing efforts until it saw substantial improvement in the jobs market.
The bank added that it would also extend its "Operation Twist" scheme of selling short-term debt and buying long-term bonds with the proceeds in order to keep long-term interest rates as low as possible.
While the announcement had been expected, dealers cheered the fact that the central bank said it will continue with the policy until it feels the economy is strong enough.
"This is action aimed at helping (what is) by far the most important economy in the world," said Joe Bracken, head of macro strategies at BT Investment Management in Sydney.
"Anything that puts the US economy on the right track is greeted with applause in Asia because it's a market they all export to."
On Wall Street, investors went into a buying frenzy, sending the Dow surging 1.55 percent, the S&P 500 rallied 1.63 percent and the Nasdaq climbed 1.33 percent.
The move comes a week after the European Central Bank said it would buy unlimited amounts of debt from under pressure eurozone nations in a bid to lower their borrowing costs, which had reached dangerous levels.
"The combined actions are giving the markets a much-needed sense of stability, and should help keep share prices supported for at least the next several sessions, if not longer," Hiroyuki Fukunaga, CEO of asset manager Investrust, said.
On currency markets the euro rose above $1.30 for the first time since May before easing slightly to $1.2986 by the end of trade Thursday.
In early Tokyo action the single currency was back up again, buying $1.3007, while it was also at 100.93 yen, compared with 100.61 yen in New York.
And the dollar was at 77.62 yen from 77.48 yen in the United States, where it sank at one point to a seven-month low of 77.13 yen.
The US unit was given support by concerns Japanese authorities would step in to weaken the yen.
Finance Minister Jun Azumi said he would not rule out any policy options to fight excessive moves in the yen, which hurts exporters when it rises too much.
Traders also said the central bank carried out a rate check with several lenders during New York trade, the first since June, Dow Jones Newswires said.
After checking the yen exchange rate with several banks, the bank of Japan could immediately follow with an intervention.
Oil prices rose, with New York's main contract, light sweet crude for delivery in October advancing 69 cents to $99.00 a barrel and Brent North Sea crude for November delivery adding 49 cents to $116.37.
Gold was at $1,772.70 at 0300 GMT compared with $1,730.63 on Thursday.