Wall Street bounced back from big losses last week, when the Federal Reserve kept interest rates unchanged over worries about the global economy.
Chinese shares rose despite local reports that a government think tank says the economy will slow this year.
The Chinese Academy of Social Sciences expects growth to slow to 6.9% this year, below the government's 7% target.
In its "blue book" report, the academy said that China's financial markets needed more time to develop and transform, according to Shanghai Securities News.
Also on Tuesday, the Asian Development Bank said it expected China's economy to grow by 6.8% this year, and slow to 6.7% in 2016.
The Shanghai Composite closed up 0.9% at 3,185.62, while Hong Kong's Hang Seng index ended 0.2% higher at 21,796.58.
Investors are also looking ahead to a preliminary factory activity survey due on Wednesday for clues on the extent of the slowdown in the world's second largest economy.
In Australia, the benchmark S&P/ASX 200 index closed up 0.7% at 5,103.55, with investors welcoming data that showed property prices rose the most in five years during the second quarter.
Residential property prices in the country's eight capital cities rose 4.7% on the quarter, the biggest increase since the last quarter of 2009.
That led to an annual increase of 9.8%, compared with 6.9% in the first three months of the year.
Trading in the rest of Asia was lighter than usual with the region's biggest market, Japan, closed until Wednesday for public holidays.
South Korea's Kospi index ended up 0.9% at 1,982.06.
Shares in carmakers Hyundai and Kia rose more than 3% after the government said it would investigate Volkswagen's diesel cars over the emissions rigging scandal.
VW has admitted to rigging emissions tests in the US.
Asian markets headed higher on Tuesday, recovering from the previous session's losses, after US shares rebounded.