In South Korea, unexpectedly strong growth figures also weighed in to boost investor confidence.
The country's benchmark Kospi index closed up 0.7% at 2,040.40 points on news that economic growth hit a five-year high in the third quarter of the year.
In Tokyo, the Nikkei 225 index jumped 2.1% to finish at 18,825.30 points.
Stocks were lifted in Japan by the positive signals coming overnight from the European Central Bank as well as the strong close on Wall Street.
A weaker yen also suggested a good day for the country's crucial export sector.
Car maker Toyota and electronics giants Sony and Toshiba all saw solid gains of as much as 2%.
Elsewhere in Asia, Hong Kong's Hang Seng closed up 1.34% at 23,151.94, while the benchmark Shanghai Composite on China's mainland closed up 1.3% at 3,412.43.
Australia's S&P/ASX 200 finished 1.7% higher at 5,351.60 points.
The country's large lenders, Westpac, CBA and ANZ, jumped by as much as 2%, while commodity producers' shares were also up.
Mining giant BHP Billiton rose by more than 2% while Santos continued yesterday's rally with another 2.2% increase.
Shares across Asia rallied on Friday on news that the European Central Bank is considering more economic stimulus.