South Korea's Kospi added 32.66 points, or 1.58 percent, to 2,097.18 while the Kosdaq gained 7.30 points, or 1.07 percent, to 690.39.
In Japan, the benchmark Nikkei 225 added 195.59 points, or 0.96 percent, to 20,555.29 after resuming trade on Tuesday — the Japanese market was closed Monday for a public holiday.
Greater China markets gained: Hong Kong's Hang Seng index rose 1.82 percent in late-afternoon trade, while mainland Chinese markets rose as the Shanghai composite added 34.58 points, or 1.36 percent, to 2,570.34.
Major indexes in Singapore and India also rose.
Australia's ASX 200 was up 41.20 points, or 0.71 percent, at 5,814.60 as the heavily-weighted financial subindex added 0.66 percent while the energy and materials sectors also posted gains.
Meanwhile, the Australian dollar traded at $0.7216 as of 3:42 p.m. HK/SIN, climbing from an earlier low of $0.7188.
"Risk is under modest downward pressure after yesterday's disappointing December Chinese export data and confirmation of weak euro area industrial production fuelled concerns that a synchronised global manufacturing down-swing is underway and possibly intensifying," analysts at ANZ Research wrote in a Tuesday morning note.
The analysts added that resolving trade uncertainty is "fundamental" to stabilizing the outlook, referring to an ongoing trade dispute between Washington and Beijing.
The British pound traded at $1.2885 as of 3:46 p.m. HK/SIN, climbing from levels below $1.2740 in the previous week. Sterling will be a focus for investors as lawmakers vote on U.K. Prime Minister Theresa May's Brexit deal to leave the European Union.
The vote is widely expected to be defeated in parliament Tuesday, but could potentially still trigger a violent market reaction, according to some analysts.
"Today's vote is considered a 'buy the rumour, sell the fact' play for the pound especially if the Brexit agreement is defeated by more than 100 votes," analysts at Singapore's DBS Group Research wrote. "It is still too early to take off the risk for the pound to fall to its post-referendum low near 1.20 this year."