London's top tier powered 95.6 points ahead to 5915.6 - a 1.6% rise - while the Dow Jones Industrial Average on Wall Street made further gains after a 1.5% surge overnight.
The Fed cheered investors with its third round of quantitative easing - worth 40 billion US dollars (£25 billion) a month - to boost the US jobs market.
It said on announcing the measures after London's market close yesterday it would continue to pump money into the economy until employment improves.
Kathleen Brooks, research director at Forex, said: "Markets like what they heard from Fed chairman Ben Bernanke yesterday and the extension in the risk rally has gathered speed."
With the dollar weakened by the launch of so-called QE3 in the US, the pound continued to rise against the greenback, up 0.6% at 1.62 dollars.
But sterling remained down against the euro, at 1.24 euros.
The Fed's move inspired an appetite for risk among traders with miners filling the risers board, while Britain's banks also enjoyed a decent run.
Copper giant Kazakhmys topped the Footsie with a 14% surge, adding 93p to 773p, while Vedanta Resources was 128.5p higher at 1090p and Evraz was up 34.3p at 293.7p.
Barclays rose 11.1p to 229.1p in the banking sector, while Lloyds Banking Group was 1.1p ahead at 40p and HSBC rose 16.3p to 584.4p.
Royal Bank of Scotland was 2% ahead as it fired the starting gun on its flotation of Direct Line Group, which owns the brands Churchill and Privilege.
The move, which has been driving a rise in the share price in the last few sessions, will see around 25% or more of Direct Line Group offered in the initial share sale. Shares were up 5.1p at 279p.
BSkyB, beaten by telecoms giant BT to a £152 million rugby television rights deal earlier this week, dropped 24p to 720p despite buying back another 350,000 shares.
Pharmaceutical stocks fell out of favour as investors ditched more defensive investments, with GlaxoSmithKline falling 22p to 1417.5p, AstraZeneca losing 19.5p to 2893p and Reckitt Benckiser dropping 62p to 3572p.
In a session of slim pickings for corporate results, pubs group JD Wetherspoon took centre stage with full-year profits of £58.9 million, a drop of 4.1%.
Shares jumped 3%, up 15.1p to 475.7p, as its pubs showing the London 2012 Olympic and Paralympic Games helped like-for-like sales jump 8.4% in the six weeks to September 9, with total sales up 12.8%.
But analysts warned traders not to buy "aggressively" as margin pressure is likely to resume as normal trading conditions return.
The biggest Footsie risers were Kazakhmys up 93p to 773p, Vedanta Resources ahead 128.5p to 1090p, Evraz up 34.3p to 293.7p and Eurasian Natural Resources up 35.7p to 363.2p.
The biggest Footsie fallers were BSkyB down 24p to 720p, Reckitt Benckiser off 62p to 3572p, BT Group down 3.8p to 233p and GlaxoSmithKline down 22p to 1417.5p.
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