The rally follows a slight easing of trade tensions between the U.S. and China after they agreed to refrain from new tariffs pending a new round of negotiations. That has relieved some pressure on markets, though the trade war still overshadows the global economic outlook.
Japan's Nikkei 225 index added 0.3% to 21,707.65, while the Shanghai Composite index edged 0.1% higher to 3,017.26. In Hong Kong, the Hang Seng gained 0.4% to 28,985.55, while the S&P ASX 200 in Australia rose 0.6% to 6,724.40.
Shares rose in Taiwan, Singapore and Indonesia in Malaysia.
On Wall Street, investors extended a rally through a holiday-shortened day, with the S&P 500 index gaining 0.8% to close at 2,995.82, the third record high close in as many days.
The Dow Jones Industrial Average also reached a record, gaining 0.7% to close at 26,966. A rally in technology shares pushed the tech-heavy Nasdaq composite 0.8% higher to 8,170.23.