Seoul's Kospi index was up 5.4 percent, and Hong Kong's Hang Seng index surged 3.9 percent and Singapore's Straits Times Index jumped 3.9 percent. Key indexes in Australia and Taiwan were also higher.
The U.S. Treasury's decision Sunday to place the two companies, which own or guarantee about half of U.S. mortgage debt, into a conservatorship removes a big cloud that had been weighing on global markets.
"I think what the American authorities have done, in the brief look I've had, it is the right thing," said Glenn Stevens, the head of Australia's central bank, at an appearance before a parliamentary committee in the southern city of Melbourne.
"Their implications are likely to be positive for markets because it's a source of uncertainty close to resolution," he said.
U.S. futures signaled that Wall Street was poised to advance Monday as well. The Standard & Poor's futures index was up more than 2 percent.
Japanese officials also hailed Washington's bailout.
"We welcome the plan as an appropriate measure as it is believed to contribute to stabilizing the financial markets," Chief Cabinet Secretary Nobutaka Machimura was quoted as saying by Kyodo News.
Jacky Choi, a Hong Kong-based fund manager at Value Partners Ltd., which manages about $5 billion in Asia, said the U.S. move comes as a relief to the many Asian governments and institutions with the mortgage giants' debt on their books.
He added, however, that Monday's surge in equities didn't necessarily foreshadow a broader turnaround and noted that trading volumes weren't very large in some markets. Many investors were still hesitant to place long-term bets, he said.
"There's not really a sentiment change. People are still reluctant," Choi said. "It takes time for sentiment to recover in a market like this."
For now, the news injected life into recently listless banking names, with the Commonwealth Bank of Australia up 5.9 percent and National Australia Bank 7.8 percent higher.
In Tokyo, Mizuho Financial Group and Mitsubishi UFJ Financial Group both gained more than 12 percent. Sumitomo Mitsui Financial Group skyrocketed almost 17 percent.
The three major banks said they each had about 200 billion yen ($1.8 billion) in exposure to Freddie Mac and Fannie Mae bonds, but declined to comment on the bailout.
Nomura Holdings, Inc. jumped 9.1 percent following weekend reports that Japan's largest brokerage group is considering buying a stake in U.S. investment bank Lehman Brothers. Nomura has funds exceeding $1.87 billion for investment in U.S. and European financial institutions and is considering Lehman as one of its investment candidates, Nomura President Kenichi Watanabe was quoted as saying by the Japanese newspaper Yomiuri.
In Hong Kong, HSBC soared 4.5 percent and No.1 China lender ICBC rose 4.7 percent.
Bucking the regional trend was China's Shanghai Composite index, which was down more than 2 percent on heavy losses in property developers, refiners and airlines. But major banks rose, with Bank of China up 2.3 percent, and Industrial & Commercial Bank of China adding 0.7 percent.
Elsewhere, Taiwan's key index shot up 5.6 percent, while India's Sensex jumped 3.9 percent.
Monday's gains in Asia follow a dismal trading session Friday when concerns about the U.S. economy and its impact on global growth sent markets tumbling across the region.
In currencies, the dollar was mixed. It climbed to 108.72 yen from 107.72 yen late Friday, but fell against the euro, which rose to $1.4371 from $1.4266.
