Japan's benchmark Nikkei average closed up 1.41 percent at 10,080.1 on Tuesday, while the broader Topix gained 0.6 percent to 838 points.
Shinzo Abe, who is set to become prime minister on Wednesday, renewed pressure on the Bank of Japan (BOJ) to adopt a higher inflation target. Abe said he would try to revise a law guaranteeing the BOJ's independence if his demand for a binding 2 percent inflation target - double its current goal - is not met.
(Read More: Japan's Deflation Battle—Why This Time Is Different)
Exporters led the gains, with Honda Motor adding 1 percent, Fanuc rising 2.3 percent and Canon gaining 2.1 percent.
Mitsubishi Chemical was up 1.7 percent after news that the firm will buy Qualicaps, a drug capsule maker, from U.S.-based Carlyle Group.
Mitsubishi Electric dropped 4 percent after it pledged on Friday to pay a total 77.3 billion yen ($912 million) to several Japanese government agencies for over billing for equipment and services over several decades and slashed its annual profit forecast by a quarter.
Chinese shares closed up more than 2 percent at their highest in over five months on Tuesday, extending their uptrend since early this month, as investors bought property stocks on increasing optimism about the sector.
The CSI300 index of the top Shanghai and Shenzhen listings closed
up 2.8 percent at 2,448.4 points, while the Shanghai Composite Index was up 2.5 percent at 2,213.6 points. Both indices closed at their highest since early- or mid-July.
Property shares outperformed with China Vanke, the country's largest real estate developer by sales, ended up 6 percent while its nearest rival Poly Real Estate rose 4.7 percent.
The country's reviving economy and strong demand for housing are likely to put upward pressure on prices next year, a Reuters poll showed last week.