MSCI's broadest index of Asia-Pacific shares outside Japan rose 0.2 percent.
South Korea's KOSPI gained 0.5 percent and Japan's Nikkei climbed 1 percent.
Asia took its cue from Wall Street, where the Dow and Nasdaq each rallied about 1.5 percent overnight on optimism over U.S.-China trade negotiations and a tentative U.S. congressional spending deal to avert another partial government shutdown.
U.S. President Donald Trump said on Tuesday that he could see letting the March 1 deadline for reaching a trade agreement with China slide a little if the two sides were close to a complete deal.
Officials in Washington and Beijing had expressed hopes that a new round of talks which began this week would bring them nearer to easing their seven-month trade war.
"We are currently seeing negative sentiment which had built up over trade concerns and U.S. fiscal issues being unwound," said Soichiro Monji, senior economist at Daiwa SB Investments in Tokyo.
"For risk assets to move purely on optimism, the U.S.-China trade row will need to see some kind of a closure in March. A more permanent solution to avoid a U.S. government shutdown is also necessary. It has to be remembered that we are not there yet."
U.S. congressional negotiators cobbled together a tentative bipartisan border security deal late on Monday to avert another partial government shutdown. However, Trump on Tuesday expressed displeasure with the agreement and said he had yet to decide whether to support it.
With risk aversion ebbing for the time being, safe-haven government bonds were sold and their yields rose. The 10-year U.S. Treasury note yield extended an overnight rise and edged up to a near one-week high of 2.694 percent.
The dollar was on the defensive as investors shifted their money to riskier assets amid the U.S.-China trade-talk hopes.
The dollar index stood at 96.701 after its eight-day winning run came to an end overnight to push it away from a two-month peak.
The euro was a shade higher at $1.1333 having gained 0.5 percent the previous day, when it bounced from a three-month low of $1.1258.
The dollar was steady at 110.53 yen.
In commodities, U.S. crude oil futures were up 0.73 percent at $53.49 per barrel after rallying 1.3 percent on Tuesday.
Oil prices surged on Tuesday after OPEC figures showed it cut production sharply in January, and as lead member Saudi Arabia said it would reduce its output in March by an additional 500,000 barrels.- Reuters
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