If sustained it would be the biggest daily rise for the Nikkei since late 2016.
MSCI's broadest index of Asia-Pacific shares outside Japan added 1.2 per cent, though that followed a drop of nearly 6 per cent on Monday.
The numbers were certainly large, with analysts estimating the package could make $4 trillion or more in loans to non-financial firms.
The purchases would be made, it said, "in the amounts needed to support smooth market functioning and effective transmission of monetary policy to broader financial conditions and the economy".
The Fed's package helped calm nerves in bond markets where yields on two-year Treasuries hit their lowest since 2013, while 10-year yields dropped back to 0.79 per cent.More news: Cuomo warns coronavirus infection rates are rising faster than expected
Goldman Sachs warned the US economic growth could contract by 24% in the second quarter, two-and-a-half times as large as the previous post war record.
Business activity collapsed from Australia and Japan to Western Europe at a record pace in March as nations locked down to curb the spread of the disease, shuttering shops, restaurants and offices.
Hundreds of thousands of people have already filed for unemployment insurance in California alone, the state's governor said at the weekend, and many analysts are projecting declines in economic output next quarter that are far worse than the steepest drop during the Great Recession.
The measures go beyond those used during the 2008 financial crisis. This might suggest that the strong uptrend remains intact despite short-term downside.
The US dollar eased just a touch on the yen to 110.90 after hitting a one-month top at 111.59 on Monday, while the euro inched up to US$1.0754 from a three-year trough of US$1.0635.More news: Why Oprah and Stedman quarantined separately
The series of actions marks a massive intervention by the US central bank beyond the financial markets where it has so far concentrated its firepower into the real USA economy.
Against the U.S. dollar, the single currency jumped 1.5 per cent to US$1.0880, a three-day high.
Commodity and emerging market currencies that suffered most during the recent asset rout, also benefited from the Fed's steadying hand.
Spot gold jumped 3.5 percent to $1,607.05 per ounce, after rising 3.7 percent on Monday, the highest percentage gain since June 2016.
Oil prices also bounced after recent savage losses, with U.S. crude up $1.09 at $24.45 barrel.More news: India's 1.3 billion people go into full lockdown from midnight (24)
Earlier in the session both Brent and WTI were trading up over 5 per cent. USA gasoline futures, meanwhile, soared over 30 per cent earlier in the day and were now trading up around 14 per cent.