U.S. Senate and House leaders passed a bill to end the fiscal impasse late on Wednesday, hours before the government's borrowing authority was due to expire. The deal will fund the government until January 15 and raise the debt limit through to February 7. However, this means there is still a risk of another shutdown early next year.
Indonesia's Jakarta Composite rose 0.8 percent, while Thailand's SET and China's Shanghai Composite gained around 0.7 and 0.6 percent, respectively, in the morning trading session on Thursday.
(Read more: Why emerging markets look good amid the shutdown)
Tim Riddell, head of global markets research, Asia, at ANZ says while the current scenario is "supportive" for risk appetite, investors are unlikely to be "gung ho" due to this uncertainty. Nevertheless, he expects both Asian and U.S. markets to continue their uptrend for the remainder of the year, barring any new political developments.
One point of comfort is that under the agreement to reopen the government, the House and Senate have been directed to hold talks and produce a 10-year tax and spending blueprint by December 13, he said.
Kelly Teoh, market strategist at IG says the bigger picture for investors now is that U.S. monetary stimulus is here to stay for a while longer, which will mean more liquidity trickling into emerging markets.
(Read more: Forget tapering, emerging markets need to watch the wages)
Market watchers expect the Federal Reserve will delay plans to wind down its $85 billion-a-month asset-purchase program to 2014 following the 16-day partial government shutdown and political stalemate on the debt ceiling. Before the political debacle, most economists expected the central bank would begin tapering in December 2013.
"It will be risk-on, the speed and velocity of that will slowly increase. The emerging market Asian space will be a key beneficiary, despite their structural issues," Teoh said.
— CNBC's Ansuya Harjani; Follow her on Twitter @Ansuya_H