The US central bank said it would buy $40 billion of mortgage debt a month and kept interest rates at below 0.25%.
It said it would also continue its programme to reduce long-term borrowing costs for firms and households.
Japan’s Nikkei 225 index rose 1.8%, South Korea’s Kospi gained 2.6% and Hong Kong’s Hang Seng added 2.5%.
This followed gains of 1.6% rise in the Dow Jones and S&P 500 indexes on Thursday.
Investors are hoping the measures will revive growth in the US economy, the world’s biggest, and a key market for Asian exports.
“They’re saying that the punch bowl, the fuel for the economy, isn’t going away – it’s going to be here as long as you need it,” said Tony Fratto, managing partner at Hamilton Place Strategies, a policy consulting firm.
There have been growing fears about the global economy with a weak recovery in the US and the ongoing debt crisis in the eurozone.
The slowdown in China’s economy, the world’s second-largest, and one of its biggest drivers of growth after the global financial crisis, has fanned those fears.
Prompted by these concerns, policymakers in these regions have been taking measures to try to spur a fresh wave of growth.
The Federal Reserve’s announcement came days after the European Central Bank (ECB) announced its latest plan.
Last week, the ECB said that it would buy bonds from the bloc’s debt-ridden nations in an attempt to bring down their borrowing costs.
Meanwhile, China has cut its interest rates twice since June to bring down borrowing costs for businesses and consumers. Beijing has also lowered the amount of money that banks need to keep in reserve three times in the past few months to further encourage lending.
This week South Korea has also unveiled two stimulus measures aimed at boosting domestic demand and helping small businesses.
Analysts said the moves had helped reassure investors and markets that policymakers were doing all they could to ensure growth in the global economy.
“You’re witnessing global economic stimulus across the board,” said Quincy Krosby, a market strategist at Prudential Financial.
“The Fed’s actions are occurring in conjunction with the European Central Bank’s commitments to support the euro and amid talk that China could also deliver a stimulus package.”
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