Investors were also encouraged by Wall Street's gains Monday, while U.S. stock index futures were pointing to strong open Tuesday in New York.
The Barclays news "immediately raised hopes that banks may be able to weather the current risks facing the global financial sector," said Motomi Hiratsuka, head of sales trading at BNP Paribas in Tokyo. "But it remains to be seen how long this (boost in sentiment) will last."
Japan's Nikkei 225 jumped 378.93 points, or 4.9 percent, to 8,105.62, while Australia's S&P/ASX200 index rose 3 percent to 3,444. India's Sensex also rose, gaining 2.5 percent to 8,888.04.
Shares in Barclays surged more than 70 percent Monday after the bank said it expects pretax profits for 2008 to be well over 5.3 billion pounds ($7.3 billion), despite 8 billion pounds of asset writedowns at its investment banking division.
In a joint letter to reassure investors, the bank's chairman Magnus Agius and chief executive John Varley said the bank did not need any more capital injections to cover potential losses associated with the global financial turmoil.
Dutch bank ING provided an extra fillip for banking stocks, jumping nearly 28 percent after it said it would get a government backstop for 80 percent of a 27.7 billion euro ($36.4 billion) portfolio of risky assets.
Major Japanese financial stocks rose in the wake of gains in European banks. Mitsubishi UFJ Financial Group jumped 8.3 percent, while Sumitomo Mitsui Financial Group Inc. rose 8.1 percent.
Several of the region's biggest markets, including Hong Kong and South Korea, remained shut for the Lunar New Year holiday. Markets in mainland China, Singapore, Malaysia and Taiwan were also closed.
Buoyed by the positive banking news, European markets surged overnight, with Britain's FTSE 100 gaining 3.9 percent to 4,209.01, while Germany's DAX climbed 3.5 percent at 4,326.87.
On Wall Street, the Dow Jones industrials zigzagged to a higher close, ending up 0.5 percent at 8,116.03. Stocks rose in response to Pfizer Inc's $68 billion planned acquisition of Wyeth, a deal that reassured investors that mergers could still take place in a recession.
Dow futures were up 97 points, or 1.2 percent, to 8,134, while S&P 500 futures were up 10.2 points, or 1.2 percent, at 841.
Markets in Singapore and South Korea will reopen Wednesday, and Hong Kong's markets will reopen Thursday. Trading in mainland China and Taiwan will be closed all week and resume Feb. 2.
Oil prices, meanwhile, hovered just above $46 a barrel as traders weighed waning demand and OPEC's compliance with production cuts. Light, sweet crude for March delivery was up 48 cents at $46.21 a barrel in electronic trading on the New York Merchantile Exchange.
In currencies, the dollar edged up to 89.49 yen from 89.25 late Monday, whiel the euro rose to $1.3225 from $1.3201.