Shares in the US, which have been on the slide for the past few months, surged as news of the new 6% rate broke, with the technology-laden Nasdaq going on to record the biggest rise in its history.
The decision came four weeks earlier than expected and stunned markets and analysts across the world.
It will increase the pressure on other central banks to cut interest rates in an attempt to head off a global economic slump.
Shares in the US, which have been on the slide for the past few months, surged as news of the new 6% rate broke, with the technology-laden Nasdaq going on to record the biggest rise in its history.
Germany's benchmark DAX exchange - the only exchange in Europe still open when the news broke - also surged sharply.
Stock markets in Asia also generally rose when they opened on Thursday, with the tech heavy Korean and Taiwanese stock markets rising 7.5% and 5.4% respectively.
In Hong Kong the Hang Seng index was more than 4% higher, Singapore's Straits Times index was up 3.1% and Australia's All Ordinaries rose 1.5%.
The exception to the general mood was Japan, where Tokyo's benchmark Nikkei 225 index closed down 0.6% as gloom over its domestic economy outweighed the lift provided by the rate cut.
Other stock markets in Europe are expected to follow the upwards trend when they open on Thursday.
Bush pleased
The Federal Reserve had not been expected to cut interest rates until its Open Market Committee meeting at the end of January.
President-elect George W Bush said he was pleased with the Fed's decision.
When asked whether the rate reduction would make it tougher to forge ahead with his tax cut plan, Mr Bush said: "Not in the least."
The last time the Fed took such dramatic action was in the midst of the Asian crisis in 1998.
Consumer confidence
The move is being seen as a sign of the growing fears that the US economy may be heading for a hard landing, or even recession, rather than the gentle slowdown policymakers want.
Techmark 100: at lowest level since Nov 1999
Cac 40: at lowest level for a year
It ended up 324.82 points, or 14.17%, up to close at 2,616.56.
The blue chip Dow Jones Industrial Average closed up 2.88% or 310.28 points at 10.956 points, its highest close in two months.
The dollar also rallied against the euro, with $0.93 buying one euro.
In a statement, the Federal Reserve said the action was taken "in light of further weakening of sales and production and in the context of lower consumer confidence".
Bond chief 'flabbergasted'
It said it was prepared to make further cuts if necessary to prevent the US economy slowing down.
It was the first 0.5% cut in that rate since mid-1992.
The move provoked widespread astonishment from market-watchers.
"I am flabbergasted. I had to do a double take on the screen. The bond market was anticipating this - but clearly not today," said Brian Robinson, senior bond strategist at 4Cast, New York.
"On top of NAPM, on top of yesterday's 7% decline in the Nasdaq, and horrible sales from Ford, maybe they just figured what is the point of waiting... It almost smells like these guys are a little bit panicked."
European reaction
The only European market still open when the announcement was made, Frankfurt, saw its benchmark Dax index rose 6% within minutes of the announcement.
The late rise was in contrast to a day which had seen stocks fall worldwide after the Nasdaq recorded a 7.2% loss on Tuesday.
This index had lost more than 55% of its value since March 2000, and was back to the levels of two years ago.
European stock markets had all been dragged lower with some hefty losses suffered in the hard-pressed internet, computer and telecoms sectors.
In London the benchmark FTSE 100 index slumped more than 2% to 6,039.9 points - close to the 6,000 barrier last breached in October 1999.
The Techmark 100 index of UK technology companies fell more than 6.5% to close at 2,344.6 - its lowest level since launch in November 1999.
Individual stocks which suffered in London included Vodafone, down 6% to 225p, and Colt, 81p lower at 1,290p, BT down 12p at 560p and Baltimore Technologies, down 34p at 285p.
In Paris the benchmark Cac 40 index slumped more than 2% to close at 5,684, its lowest level for about a year.