At 09.25 a.m., the Sensex traded 327 points or 1.8 per cent higher at 18,348 while the Nifty advanced 101 points to 5,536.
"Markets are expected to consolidate around 5,550-5,630 levels, which are crucial resistance areas, beyond which stocks would go much higher," independent analyst Sarvendra Srivastava said.
The Fed said it would buy $40 billion of mortgage securities a month until the US economy improves. Fed's decision would lead to a rise in liquidity in the global economy giving a push to riskier assets like equities and commodities.
The government's decision to hike diesel prices also cheered markets. Investors have been concerned over the rising subsidy bill because state-run oil refiners have been selling fuel at below market prices. Shares in OMCs - BPCL, IOC and HPCL - traded with 2-3 per cent gains.
"This is more than what we can handle right now. Domestic cues have come last evening. I just hope the government sticks to the fuel price hike. The government may allow FDI in aviation today evening. That will keep the markets running up," market analyst Ambareesh Baliga said.
The government hopes the move will help avert a sovereign credit downgrade, the prime minister's chief economic advisor, C. Rangarajan, said. "The government has shown it can take hard decisions, very difficult decisions."
The cabinet's economic panel is due to meet on Friday to discuss a plan to invite foreign airlines to invest in domestic carriers and a proposal to sell shares of large state-run firms.
However, analysts say it will not be one-way street for the markets.
"We may see aviation and retail FDI in coming weeks and if the government doesn't deliver, markets may witness a pullback. High crude prices may also be a drag on Indian equities. Coal and power are well known risks," Saurabh Mukherjee, head of equities at Ambit Capital told NDTV Profit.
US markets staged a huge rally Thursday after investors got the aggressive economic help they wanted from the Federal Reserve. The Dow Jones industrial average spiked more than 200 points and cleared 13,500 for the first time since the beginning of the Great Recession. The average is within 625 points of its all-time high.
Asian shares rose to a four-month high on Friday after the U.S. Federal Reserve announced an aggressive new stimulus to drive job creation in the U.S. economy.
The Fed's move will likely accelerate the risk-positive momentum at work since the European Central Bank's bond-buying scheme to get borrowing costs down for euro zone members was approved by Germany's constitutional court.
Japan's Nikkei stock average opened up 1.1 percent.
(With inputs from agencies)