MSCI's broadest index of Asia-Pacific shares outside Japan rose 0.4 percent while Japan's Nikkei jumped 1.7 percent.
U.S. new home sales data out on Tuesday showed a jump in April to their strongest monthly pace in more than eight years, with prices setting record highs.
Coming after a raft of positive U.S. data and comments from various Fed officials explicitly highlighting a chance of a Fed rate hike in June or July, the data helped to cement the case for a rate hike in coming months.
The yield on policy-sensitive two-year U.S. notes rose to a 10-week high of 0.930 percent. U.S. interest rate futures are pricing in more than 60 percent chance of a rate hike by July, compared to around 20 percent about 10 days ago.
"There appears to be a consensus among Fed policymakers that they have to put a rate hike back on the table because markets had been pricing in almost no chance of a rate hike," said Koichi Yoshikawa, executive director of financial markets at Standard Chartered Bank.
Higher interest rates benefit financial shares as they increase interest income, helping to lift bank shares.
On Wall Street, S&P 500 Index rose 1.4 percent, helped by high-tech and bank shares.
European shares gained sharply overnight, led by financial shares, with the pan-European stock index rising 2.3 percent to its highest level since late April.
The news flows in Europe were generally positive for investor sentiment.
A UK poll showed a 13-point lead in support among Britons to stay in the European Union over their "Leave" rivals while Greek bond yields hit six-month lows as European finance ministers appeared likely to approve new loans to Athens.
In a major breakthrough, euro zone finance ministers also agreed a deal with Greece and the International Monetary Fund in the early hours of Wednesday that will address Athens's requests for debt relief.
The "Brexit" poll results helped the British pound gain 1.1 percent, its biggest daily gain in 10 weeks, on Tuesday.
The sterling traded at $1.4622, near last week's peak of $1.4663, a break of which could open the way for a test of $1.4770, its four-month peak hit in early May.
In another clear sign of easing concerns on the "Brexit", implied volatilities on sterling options also fell to lowest level in almost a month.
The U.S. dollar held firm against most other currencies thanks to expectations of a rate hike by the Fed.
The dollar strengthened to 110.09 yen from this week's low of 109.12, within sight of testing its three-week high of 110.59 touched on Friday.
The euro dropped to a 10-week low of $1.1133, shedding more than 4 percent since it hit an eight-month peak of $1.1616 in early May, showing little reaction to the news on agreement on debt relief for Greece.
The Australian dollar slipped to a 12-week low of $0.7145 on Tuesday and last stood at $0.7190 as it is pressured by expectations of a rate cut by the Reserve Bank of Australia.
Gold also hit a six-week low of $1,226.50 per ounce on Tuesday and last stood at $1,227.60.
Many emerging market currencies felt the dollar's heat but the Turkish lira jumped 1.6 percent off near four-month lows after investor-friendly deputy prime minister Mehmet Simsek kept his post in the government.
Oil prices held firm, helped by a rise in overall risk appetite and expectations of a drawdown in U.S. crude inventories.
U.S. crude futures hit a 7 1/2-month high of $49.29 per barrel in early Asian trade.
Brent crude futures rose to $49.14 per barrel, near last week's 6-month high of $49.85.
source: www.abs-cbnnews.com
