Japan's Nikkei has continued its surge, rising above the 14,000 mark for the first time since June 2008.
The benchmark index rose 3.6% to 14,180 on its first day of trading after the Golden Week holiday.
Japanese markets have jumped recently after its central bank unveiled aggressive moves, including doubling the money supply, to spur growth.
On Tuesday, markets were also reacting to last week's events, including a rate cut by the European Central Bank.
"Stocks must account for a few sessions of most positive activity in overseas markets, which have resulted in a sharply weaker yen, all of which will be tonic for buying," said Hiroichi Nishi from SMBC Nikko Securities.
"Signs that the US economy is improving, as well as the European Central Bank's rate cut are most encouraging fundamentally."
The European Central Bank cut key interest rates to an all-time low of 0.50% on Thursday. That decision came down after Japanese markets had already closed.
Meanwhile, the Japanese yen weakened further on Tuesday, another positive sign for the economy.
It was trading close to 98.97 yen against the US dollar in Asian trade, down from the near 98 yen level before the holidays.
A weak yen bodes well for Japan's exporters as it not only make their goods more affordable to foreign buyers, but also boost their profits when they repatriate their foreign earnings back home.
Shares of major exporters Toyota and Suzuki Motors, which rely heavily on overseas sales, were higher.