Markets in Taiwan, Singapore, South Korea, Malaysia and the Philippines also closed higher while India's benchmark Sensex index was up 5 per cent by midday.
The gains cap a volatile week for Asian markets, which plunged on Monday and Tuesday on worries about a slowdown in the US, a key export market and the world's biggest economy.
Stocks rebounded however after the US Federal Reserve slashed interest rates by three-quarters of a point on Tuesday.
"The panic's gone out of the market"
Angus Gluskie, White Funds Management, Sydney
Investors have also been cheered by gains in US markets, where the Dow Jones industrials rose for a second day on Thursday on data showing number of people seeking unemployment benefits had fallen for a fourth straight week.
In Japan a recovery in the dollar against the yen on Friday helped raise stocks in major exporters such as motor manufacturers Toyota and Honda, both of whom saw their shares up more than 6 per cent.
A stronger dollar boosts exporters overseas earnings.
On Thursday George Bush, the US president, had called on the US congress to enact the stimulus package legislation "as soon as possible", saying the country "needs this boost to the economy now".
The tax rebates that form part of the revival plan will put between $300 and $600 into most US taxpayers' pockets.
"The panic's gone out of the market," Angus Gluskie, portfolio manager with White Funds Management in Sydney, told Reuters as bargain-hunting on Friday helped markets regain some lost ground.
"On most people's fundamentals, a lot of stocks in the market appear to be undervalued."
Frances Lun, general manager of Fulbright Securities Limited in Hong kong, said the US plan has given a boost to Asian markets, which are now on a rebound.
"I think the most important thing is really restoring confidence," he told AP.
"If the financial market lacks confidence, they don't believe the government is doing something positive, then they will sell."