Japan's Nikkei index was up 1.17 percent led by exporter stocks, reflecting the firmer dollar against the yen. Hong Kong was flat, Sydney lost 0.35 percent in the afternoon and Shanghai edged down 0.53 percent.
US stocks closed higher on Wednesday after a surprise jump in private sector jobs and solid growth in the service sector.
The dollar held firm against the yen in Asia, edging up to 83.27 yen in Tokyo morning trade from 83.24 yen in New York late Wednesday.
The euro fetched $1.3151 against $1.3150 the previous day. The single European currency also rose against the Japanese unit, to 109.51 yen from 109.42 yen.
Ahead of monthly jobs figures due on Friday, US private payrolls firm ADP reported that the US private sector added 297,000 jobs in December, more than three times the number created in November.
However, Australia's floods, which have hurt mining firms in particular, continued to spook the Sydney market.
According to IHS Global Insight, the floods have led to the closure of an estimated 90 million tonnes of annual production capacity.
"Australia is continuing to limp despite the fact that we are well positioned for continuing growth in China and the Asian region," Justin Gallagher, head of domestic sales trading at RBS in Sydney, told Dow Jones Newswires.
"We saw some good data out of the US last night... But there has been an enormous amount of press around the flood situation and the impact on the local economy, and investors are a little concerned about what that means."
In Hong Kong, developer stocks outperformed after a report that blue chip property firm Cheung Kong is planning the city's first yuan-denominated initial public offering, of a real-estate investment trust, in the first quarter.
In Shanghai, energy stocks slipped back after strong gains around New Year, with China Coal down 0.8 percent after gaining 6.4 percent over the previous four sessions.
In New York earlier, the Dow Jones Industrial Average rose 0.27 percent, the broader S&P 500 index gained 0.50 percent and the tech-rich Nasdaq climbed 0.78 percent.
Oil prices were mixed, despite a sharp fall in US crude inventories adding to the mood of recovery.
New York's main contract, light sweet crude for February delivery, was up 11 cents at 90.41 dollars per barrel. Brent North Sea crude for February was down five cents at 95.45 dollars.
Gold opened lower at $1,375.00-$1,376.00 an ounce in Hong Kong, down from Wednesday's close of $1,383.50-$1,384.50.