Japan's Nikkei 225 rises 1.5% to hit a new record with Takaichi all set to become prime minister

Japan's benchmark Nikkei 225 rose 1.5% to a fresh record, after closing at an all-time high Monday. The Topix also added 0.73% to hit a record high.

Broader Asia-Pacific markets also opened higher, tracking Wall Street gains led by a rally in Apple shares.

Investors await Japan's parliamentary vote, which is likely to see Sanae Takaichi become the country's next prime minister, after the right-wing opposition Japan Innovation Party said Monday it was ready to back her premiership.

South Korea's Kospi index jumped over 2%, led by gains in heavyweight auto stocks, to hit a fresh high. Shares of Hyundai Motor climbed 6.45%, while Kia Corp added 4.28%.

Australia's ASX/S&P 200 rose 0.50%. Shares of the country's rare earth companies rose after Prime Minister Anthony Albanese and U.S. President Donald Trump signed a critical minerals agreement Tuesday, aimed at countering China's dominance.

Australia's Lynas Rare Earths added 3.8%, Iluka Resources jumped nearly 6%, Pilbara Minerals rose 4.7%. VHM skyrocketed over 30%, while Northern Minerals soared nearly 15%.

Hong Kong's Hang Seng Index rose 1.17% in early trading, while the Hang Seng Tech index was up 1.84%. Mainland's CSI 300 was 0.3% higher.

Hong Kong-listed shares of CATL gained 4.73% after the battery manufacturer posted strong third-quarter earnings late Monday. The Tesla battery supplier's net profit for the July-September period rose 41% to 18.5 billion yuan ($2.6 billion).

Indian markets are closed for a holiday.

U.S. equity futures were little changed in early Asian hours, ahead of a busy earnings week from big-name companies and inflation data.

Overnight, the three key benchmarks in the U.S. rose on a rally in Apple shares after Loop Capital upgraded it to buy from hold.

 The Dow Jones Industrial Average closed 515.97 points, or 1.12%, higher at 46,706.58. The S&P 500 also climbed 1.07% to settle at 6,735.13, while the Nasdaq Composite advanced 1.37% to settle at 22,990.54.

— CNBC's Sean Conlon and Pia Singh contributed to this report.