Tokyo's Nikkei .N225 sped to a six-year peak, adding about 0.8 percent and topping the 16,000-mark, driven by buying from long-only investors after Wall Street marched upwards. Japan's benchmark was up more than 50 percent this year, on track for its best annual rise since 1972.
"Hedge funds are pretty quiet. A lot of them have closed their books for the year, so if hedge funds are quiet there is really no shorting going around in the market at the moment," a trader at a European bank in Tokyo said.
The Australian market .AXJO added about 0.6 percent, while MSCI's broadest index of Asia-Pacific shares outside Japan .MIAPJ0000PUS was up 0.2 percent.
U.S. stocks rose on Monday after data showed consumer spending rose to a five-month high last month, and the latest consumer sentiment reading showed improvement. Despite the signs of strength, inflation remains benign, with a price index for consumer spending unchanged for a second straight month.
The Dow Jones industrial average .DJI rose 0.45 percent, while the S&P 500 .SPX gained 0.53 percent and the Nasdaq .IXIC 1.08 percent.
Apple Inc's distribution deal with China Mobile lifted the technology sector, and Apple (AAPL.O) itself added 3.83 percent for the day.
Europe's FTSEurofirst 300 index .FTEU3 closed up 0.7 percent while Germany's DAX .GDAXI finished at a record.
The U.S. economic reports prompted some analysts to upgrade their forecasts for economic growth for the quarter, which in turn follows upward revisions to the third quarter.
Investors chose to focus on the strength in consumption rather than the benign inflation, and priced in slightly more risk of an earlier hike in interest rates by the U.S. Federal Reserve.
Fed fund futures were fully pricing in a move to 0.5 percent in September of 2015, compared to this time last week, when futures indicated a November hike.
Government borrowing costs have also been rising even for shorter-dated debt. Yields on two-year Treasury notes were around 39 basis points, compared to a trough of 26 basis points last month.
Rising yields supported the dollar, but it still struggled against its European counterpart. Many analysts believe the relative outperformance of the U.S. economy will benefit the dollar over time, but progress is proving to be glacial.
On Tuesday, the euro was buying $1.3686, down slightly but still holding above last week's low of $1.3623. For the year to date, the euro is holding gains of almost 4 percent against the dollar.
Both currencies have fared much better on the yen, easily the weakest of the major currencies this year as the Bank of Japan remains committed to its massive stimulus campaign.
The dollar rose 0.2 percent to 104.33 yen after hitting a five-year high of 104.63 yen on Friday, while the euro also added 0.2 percent to 142.77 yen, also near a 5-year high touched last week.
Among Asian currencies, the Thai baht fell to a low of 32.80 versus the dollar, its weakest level since March 2010. Thailand's political turmoil grew as anti-government protesters gathered on Sunday to demand Prime Minister Yingluck Shinawatra resign.
Investors also kept a wary eye on China's benchmark money market rate, after rates in China's interbank market spiked to their highest level since June in recent days due in part to seasonal factors that increase banks' demand for cash near the end of each quarter.
The seven-day bond repurchase rate CN7DRP=CFXS, opened at 5.55 percent on Tuesday, down from Monday's close of 8.90 percent. In recent days, opening trades for the seven-day repo have been considerably lower than both the previous day's close and subsequent trades on the same day, raising suspicions among traders that the central bank has attempted to guide trading.
In commodity markets, gold dipped below the $1,200 level to $1,198.50 an ounce and was heading for its biggest annual loss in three decades. It has shed nearly 30 percent so far this year and is threatening the April 2010 bottom under $1,050.
U.S. crude fell 0.2 percent to $98.67 a barrel, off a two-month high of $99.40. Benchmark Brent crude was up slightly on the day at $111.61 per barrel.