Chinese mainland markets finished up 1 percent on Tuesday, following a survey showing a pickup in China's factory activities for December.
The Shanghai composite finished up 32.64 points, or 1.05 percent, at 3,136.28, while the Shenzhen composite added 16.84 points, or 0.85 percent, to 1,985.95. In 2016, the benchmark Shanghai index had tumbled 12.3 percent, registering its worst year since 2011.
China's Caixin Manufacturing Purchasing Managers' index (PMI) rose to 51.9, compared with 50.9 in November and beating forecasts for 50.7, on the back of increased demand. A reading above 50 represents expansion in a sector, whereas a reading below 50 represents contraction.
The private manufacturing survey results came after figures at the weekend showed China's official PMI fell to 51.4 in December, slightly weaker than expectations.
In Hong Kong, the Hang Seng index was up 0.71 percent in late afternoon trade, while gaming shares fell following a decline in Macau gambling revenues. The Hong Kong benchmark had struggled to finish in positive territory for 2016, ending the year up just 0.39 percent.
Macau government data showed on Sunday that gambling revenue fell 3.3 percent in 2016, which was in line with Reuters' poll of analysts' forecasts for a decline of around 3-4 percent. One bright spot in the data was that December revenue jumped 8 percent from the previous year.
Meanwhile, Australia's ASX 200 added 1.19 percent, or 67.4 points, to close at 5,733.2, supported by broad gains across all sub-indexes. The benchmark is currently at a 16-month high, after ending 2016 up 6.99 percent, its best annual performance since 2013.
Shares of ANZ were up 1.71 percent at A$30.94 each, after the Australian lender announced it had reached a deal to sell a 20 percent stake in Shanghai Rural Commercial Bank to China COSCO Shipping and Shanghai Sino-Poland Enterprise Management Development.