Germany’s Dax and France’s CAC were 1.5% in mid-morning trading, while the UK’s FTSE rose 1%. Japan’s Nikkei 225 closed up 1.7%.
The Fed said it would scale back its $85 billion a month bond-buying programme by $10 billion a month.
Analysts said the taper was less than markets had expected.
Investors and economists have been watching closely for when the Fed would scale back its stimulus, fearing that a steep taper could undermine economic recovery.
US markets had ended sharply higher on Wednesday following the Fed’s decision. The Dow Jones jumped 292.71 points, or 1.84%, to close at 16167.97, while both the Nasdaq and S&P 500 indexes rose by more than 1%.
The stimulus programme, called quantitative easing, was introduced by the Fed after the global financial crisis.
The main objective was to increase the money supply and improve liquidity in the financial system in the hope of sparking economic growth and supporting employment.
The Fed’s governing committee cited stronger job growth as a reason for the decision to begin winding down the programme.
It forecast the unemployment rate would fall to 6.3% in 2014 from its current level of 7%.
Analysts said the Fed’s decision to scale back the programme also indicated that it was confident of a sustained recovery in the US economy.
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